differential equations formulas list pdf

Equation of a plane A point r (x, y, z)is on a plane if either (a) r bd= jdj, where d is the normal from the origin to the plane, or (b) x X + y Y + z Z = 1 where X,Y, Z are the intercepts on the axes. 91 0 obj <>stream Functions that appear at the top of the list are more like to be u, functions at the bottom of the list are more like to be dv. h�bbd```b``f�� q�d�fk��`RD�փH��`2,�fK��V0i 21-260: Diﬀerential Equations Final Exam Formula Sheet Suggestions 1. We'll assume you're ok with this, but you can opt-out if you wish. A Differentiation formulas list has been provided here for students so that they can refer to these to solve problems based on differential equations. endstream endobj startxref Second Order Linear Homogeneous Differential Equations with Constant Coefficients, Second Order Linear Nonhomogeneous Differential Equations with Constant Coefficients, Second Order Linear Homogeneous Differential Equations with Variable Coefficients, Second Order Linear Nonhomogeneous Differential Equations with Variable Coefficients, Higher Order Linear Homogeneous Differential Equations with Constant Coefficients, Higher Order Linear Nonhomogeneous Differential Equations with Constant Coefficients, Higher Order Linear Homogeneous Differential Equations with Variable Coefficients, Higher Order Linear Nonhomogeneous Differential Equations with Variable Coefficients, Linear Homogeneous Systems of Differential Equations with Constant Coefficients, Construction of the General Solution of a System of Equations Using the Method of Undetermined Coefficients, Construction of the General Solution of a System of Equations Using the Jordan Form, Linear Nonhomogeneous Systems of Differential Equations with Constant Coefficients, Linear Systems of Differential Equations with Variable Coefficients, Equilibrium Points of Linear Autonomous Systems, Linear Differential Equations of First Order, Singular Solutions of Differential Equations. The general representation of the derivative is d/dx.. v among the roots of the characteristic equation; further, Pk(t) and Qk(t) are polynomials of degree k = max(n,m). $ A��W720]�,��8 ��o =�c 69 0 obj <>/Filter/FlateDecode/ID[]/Index[45 47]/Info 44 0 R/Length 114/Prev 162259/Root 46 0 R/Size 92/Type/XRef/W[1 3 1]>>stream %PDF-1.5 %�� %%EOF h��X[O�:�+~��/� 4. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. If the power of the sine is odd and positive: Goal: ux cos i. �\i��!�,Dj�� :˿?3v�6�,mWgW��3{��o�J(1�0��S��#��E��&�b�!LHI�%LYN�#�ZG,%:�e�n tq)��p 3ZIuP+"��j"��a��DR��s�˗��GuWY�C�&f�-%�gg�u9�@��3td�d�jhs�24:�} This is half of a usual sheet of paper. 0 For the Final Exam you are allowed to bring a 8.5 × 5.5 inches piece of paper with formulas written on both sides. 45 0 obj <> endobj b`e`�dd@ A�+P�c�Re�9 ��ٳ`��bQ�m� ��y��v�|-6�J�~�p]W�� ([�7h?㋇@Z��zŮ�]`� �@ʑ��d�� oi�uc`(иj��M�N�&��ߘDa`�8��A�� t�79 First Order Differential Equations Separable Equations Homogeneous Equations Linear Equations Exact Equations Using an Integrating Factor Bernoulli Equation Riccati Equation Implicit Equations Singular Solutions Lagrange and Clairaut Equations Differential Equations of Plane Curves Orthogonal Trajectories Radioactive Decay Barometric Formula Rocket Motion Newton’s Law of Cooling Fluid … This website uses cookies to improve your experience. This might introduce extra solutions. h�b```a`` �� "Mg�� `s�@�L�� V Class 12 Maths Chapter 9 Differential Equations Formulas – PDF Download A differential equation is a mathematical equation that relates some function with its derivatives. If we can get a short list which contains all solutions, we can then test out each one and throw out the invalid ones. You can write anything you want on this formula sheet. endstream endobj 46 0 obj <> endobj 47 0 obj <> endobj 48 0 obj <>stream Variation of Parameters Method: Consider the inhomogeneous d.e. The ultimate test is this: does it satisfy the equation? If you want to learn differential equations, have a look at Differential Equations for Engineers If your interests are matrices and elementary linear algebra, try Matrix Algebra for Engineers If you want to learn vector calculus (also known as multivariable calculus, or calcu-lus three), you can sign up for Vector Calculus for Engineers This is one of the most important topics in higher class Mathematics. M�n�� 4��K�WI�py��Uzv��l8ˡ�#,��g�#��1�nG�$��K>�`[itq{ �|��&_��e;4��H��G�Q̑��a\R�K}�u6*�Gٰx��AVsN��VPp��I��9/��WӼzy��(z�SpˀW��tǯÜ�(��AX1��bR��蟥��g�u6��%��t�O�� >��Uӏ��|Ώ��}2�#�%0�3�˛��^6��A��S�ζou܍��B�a(*�*�b-�S"�u�~�~8�A� *��x��2�u�έ�!�˿�(�D�m�/��:�!L�qv "�Y�^X!`-��Q>#w��e��4|tx�C� ��S5B;5�� ^̷��wǳb�}]Lg��[6%Z��{�-�5g�s��@�/��,�@'��11�_�n�O) |"|��'�4��5�Х��H`Ԧ�@Z��{k�8wӃ�t��+�P�5��c�%��k$��9�Y��t�]��Y�3;@��Qk�ߊ.

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