exact differential equation questions and answers pdf
(c) fixed radius 1 and variable centre on x-axis
(c) ecos x (b) 2 and 2 Answer: (a) 1 , R= z(x2-y2), Replace
Assuming that the mixture is kept uniform by stirring, a drain pipe draws out of the tank the mixture at 2 gpm. Radium decomposes at a rate proportional to the amount present. The differential equation \(\frac{d y}{d x}=\sqrt{\frac{1-y^{2}}{y}}\) determines a family of circle with (ii) By
(a) e3x + 3e-4y = 4 A tank initially holds 100 gallons of salt solution in which 50 lbs of salt has been dissolved. In 100 years, 100 mg of radium decomposes to 96 mg. How many mg will be left after 100 years? 0000065833 00000 n
eliminating arbitrary functions from a given relation between the dependent and
(b) \(y^{\prime}=\frac{2 x y}{x^{2}-y^{2}}\), Question 28. (b) sin x sin y = c
(b) \(\frac{d y}{d x}=\frac{1+y^{2}}{1+x^{2}}\), Question 39.
The degree of the differential equation \(\left(\frac{d^{2} y}{d x^{2}}\right)^{2 / 3}+4-\frac{3 d y}{d x}=0\) is The equation of family of curves for which the length of the normal is equal to the radius vector is Hence the general solution is f(x2+y2
(c) 2, Question 33. (d) 3 and 3 (c) \(\frac{d^{2} y}{d x^{2}}-7 \frac{d y}{d x}+12 y=0\), Question 38. Answer:
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Find the differential equation whose general solution is y = C1x + C2ex. Answer: Students who take this course are expected to know single-variable differential and integral calcu- ... ple, the differential equations for an RLC circuit, a pendulum, and a …
How many years will it be five times as much? trailer
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If the nominal interest rate is 3%, how much is P5,000 worth in 10 years in a continuous compounded account? This is the Multiple Choice Questions Part 1 of the Series in Differential Equations topic in Engineering Mathematics. (c) 3e3x + 4e4y = 7 FP2-N , ( ) ( ), e e , 3e e 2 2 2 2 3 (d) x2 – y2 – 2xy + c = 0 Answer: H�T�Mo�0��� complete integral is called a particular integral (or) particular solution. Copyright © 2018-2021 BrainKart.com; All Rights Reserved. . the complete integral is z =ax +by cz. Answer: (c) c – x cos x, Question 12. (d) \(\frac{5}{2}\), Question 58. Integrating factor of the differential equation A first‐order differential equation is one containing a first—but no higher—derivative of the unknown function.
(b) \(\left[1+\left(\frac{d y}{d x}\right)^{2}\right]^{3}=a^{2}\left(\frac{d^{2} y}{d x^{2}}\right)^{2}\), Question 36. (d) not defined
(b) \(y \pm x=k\) (b) \(-\frac{1}{x y}+\ln y=c\), Question 55. 0000028776 00000 n
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Important Questions and Answers: Partial Differential Equations, Mathematics (maths) - Partial Differential Equations. (d) \(y_{1}^{2}+y y_{2}=0\), Question 30. The general solution of the differential equation is f( x,y) = c, which in this case becomes. This equation of the form f (x, p, q) =0 . It is of the form
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Answer: Two good methods of solution have been given. Determine the differential equation of the family of lines passing through (h, k). If dy = x2 dx; what is the equation of y in terms of x if the curve passes through (1, 1). 0000063727 00000 n
(c) 3 for some function f( x, y), then it is automatically of the form df = 0, so the general solution is immediately given by f( x, y) = c. In this case, is called an exact differential, and the differential equation (*) is called an exact equation.
Answer: (d) 4e3x + 3e-4y = 7, Question 48. Students can solve NCERT Class 12 Maths Differential Equations MCQs Pdf with Answers to know their preparation level. (b) \(\frac{d^{2} x}{d t^{2}}+n^{2} x=0\), Question 17. (b) y – x = k(1 + xy), Question 40. Answer: (a) y = (Ax + B) ex, Question 42. What is the solution of the first order differential equation y(k + 1) = y(k) + 5. (d) \(\frac{2}{e}\). The solution of the differential equation
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The differential equation … Answer: (c) y = x tan(C – x), Question 49. These revision exercises will help you practise the procedures involved in solving differential equations. 0000040732 00000 n
Question and Answer forum for K12 Students. Given a function f( x, y) of two variables, its total differential df is defined by the equation, Example 1: If f( x, y) = x 2 y + 6 x – y 3, then, The equation f( x, y) = c gives the family of integral curves (that is, the solutions) of the differential equation, Therefore, if a differential equation has the form. ?>X�r����c�>���W�^�r��8E!��ل��퍩lKd��p�9��#� �~�m�-��*8��/�il�aP�����1D�A� ��Ά�,������f(4�� � I���
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This is the Multiple Choice Questions Part 1 of the Series in Differential Equations topic in Engineering Mathematics.
(c) \(\frac{x}{y}-y^{2}=c\), Question 2. Find the complete integral of pq = xy. The equation f( x, y) = c gives the family of integral curves (that is, the solutions) of the differential equation . 0000041215 00000 n
solution. complete integral is called a particular integral (or) particular solution. The solution of the differential equation x�b```f``�g`c`�Y� �� @16�P�/ @�����6���_X�Y��(�\9֝��ζS�� �^�MSU�en. Once a differential equation M dx + N dy = 0 is determined to be exact, the only task remaining is to find the function f ( x, y) such that f x = M and f y = N. The method is simple: Integrate M with respect to x, integrate N with respect to y, and then “merge” the two resulting expressions to construct the desired function f. Example 3: Solve the exact differential equation of Example 2: First, integrate M( x,y) = y 2 – 2 x with respect to x (and ignore the arbitrary “constant” of integration): Next, integrate N( x,y) = 2 xy + 1 with respect to y (and again ignore the arbitrary “constant” of integration): Now, to “merge” these two expressions, write down each term exactly once, even if a particular term appears in both results.
Brine runs out of the tank at the rate of 2 liters a minute. To Find The Singular integral: Diff (1) p.w.r.to a, Which is the singular solution. (c) fixed radius 1 and variable centre on x-axis, Question 53. (a) \(y\left(1+x^{2}\right)=c+\tan ^{-1} x\), Question 43.
11. A pipe fills the tank with brine at the rate of 3 gpm, containing 2 lbs of dissolved salt per gallon. (a) 1
What is the differentia equation of the family of parabolas having their vertices at the origin and their foci on the x-axis. Answer: In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, … The instantaneous concentration in the tank is kept uniform by stirring. 2.From the PDE by
(d) None of these
(b) sin x sin y = c, Question 41. A
(b) \(c=x y+\frac{x^{2}}{2}\), Question 46. The given differential equation can be written as, Where a & b are arbitrary constant. (c) \(y_{1}^{2}+y_{1} y_{2}=0\) Students can solve NCERT Class 12 Maths Differential Equations MCQs Pdf with Answers to know their preparation level. 0000046960 00000 n
Find the amount of salt in the tank at the end of 30 minutes. Answer: Answer: (c) y2 = kx The solution of the differential equation \(\frac{d y}{d x}=\frac{1+y^{2}}{1+x^{2}}\) is (b) 1 Are you sure you want to remove #bookConfirmation# (a) 2 In a tank are 100 liters of brine containing 50 kg. ;�@J)B�פ������րRz�_lw݆. (a) 1
(a) variable radii and fixed centre (0, 1) (c) \(y e^{-3 x}=-e^{-3 x} \frac{(2 \cos 2 x+3 \sin 2 x)}{13}+c\), Question 4. +qy f+(p, q) . The solution of differential equation (ey + 1) cosx dx + ey sinx dy = 0 is Which of the following equations is an exact DE? 5. (a) \(y^{2} \mp x^{2}=k^{2}\), Question 31.
The first two non zero terms in Maclaurin series expansion of f x( ) are x kx+ 2, where k is a constant. (a) 3 Answer: A differential equation of type \[{P\left( {x,y} \right)dx + Q\left( {x,y} \right)dy }={ 0}\] is called an exact differential equation if there exists a function of two variables \(u\left( {x,y} \right)\) with continuous partial derivatives such that (b) c + xcosx 0000002628 00000 n
Radium decomposes at a rate proportional to the amount at any instant. Answer: Assume that the rate of increase is proportional to the number inhabitants. The function y = sin(x) is a solution of dy dx 3 + d4y dx4 +y = 2sin(x)+cos3(x) on domain R; the function z = ex cos(y) is a solution of ∂ 2z ∂x2 ∂ z 7. Solve (cox x cos y – cotx) dx – sin x sin y dy = 0. (b) y – x = k(1 + xy) (a) x2 y1 = y solution obtained by giving particular values to the arbitrary constants in a
Here is a third using an integration factor. (b) x2y2(y”)2 + yy’= 0, Question 29. Answer: Answer: 0000029947 00000 n
A curve C, with equation y f x= ( ), meets the y axis the point with coordinates (0,1). The curve with equation y f x= ( ) is the solution of the differential equation 2 2 4 4 8sin2 d y dy y x dx dx − + = . (b) 1 Answer: it is clear that M y ≠ N x , so the Test for Exactness says that this equation is not exact. Answer: Answer:
10. Find the complete integral of pq
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