Verifying the Solution of a Differential Equation

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• Verifying a solution

  It is obvious that -Ce^-t + y - 10 = 0 Y = Ce^-t + 10 So the function is the solution of the differential equation. This provides an example of verifying that a function is a solution for a differential equation.

• Stochastic differential equation

  Solution : Similar form question for (a) Similar form question for (b) This provides an example of verifying a solution for a stochastic differential equation.

• Implicit solution of differential equation

  This provides an example of verifying that an expression is an implicit solution to a first-order differential equation.

• Elementary Differential Equations : Power Series Methods

  Find two linearly independent power series solutions of the given differential equation. Determine the radius of the convergence of each series, and identify the general solution in terms of familiar elementary functions.

• Solve the differential equation or initial value problem using the method for undetermined constants and variation of parameters.

  So the solution is (2) The inhomogeneous differential equation can be separated to as And (a)The particular equation to the differential equation (*) has the form of Plug into (*) So Thus, (b) The particular equation

• Differential equations

  If the equation is an ODE, indicate whether the equation is linear or nonlinear. Write a differential equation that fits the physical description. Determine whether the given function is a solution to the differential equation.

• The Transformation of Partial Differential Equation

  The solution is in the attached file. This solution explains the transformation of the partial differential equation into a new partial differential equation by changing the variables.The solution is given in detail. 

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  value of , reduce the differential equation to and hence solve the original equation. --- Please see the attached file for the complete solution.

• Non-Homogeneous Linear Partial Differential Equation

  This solution is comprised of a detailed explanation for finding the solution of a Non- Homogeneous Linear Partial Differential Equation with Constant Coefficients.