Question

# Find the solution of the following differential equation: (?^3 y/dx^3)-7(d^2 y/dx^2)+10(dy/dx)=e^2x sinx

Find the solution of the following differential equation:

(?^3 y/dx^3)-7(d^2 y/dx^2)+10(dy/dx)=e^2x sinx

Given, ----------------(1)

First, find the solution to the homogeneous equation.

The auxiliary equation is    Hence the solution of the complementary equation is, --------------------(2)

where c1, c2, and c3 are constants.

Now we have to find the particular solution.

Using the method of undetermined coefficients, assume the particular solution as ------------(3)

Now yp(x) satisfies equation (1),

Find  Again differentiating we get,  Again differentiating the above equation we get,  Substituting the values of in (1) we get,   Equating the coefficients of like terms of x in both sides we get,  Solving the above equations we get, Hence from (3), Hence the solution of the given differential equation (1) is  #### Earn Coins

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