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Solve the differential equation using the method of variation of parameters.

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Solve the differential equation using the method of variation of parameters.

asked Feb 18, 2015 in CALCULUS by anonymous

2 Answers

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Step 1:

The differential equation is .

Solving non-homogenous differential equation:

If the differential equation is in the form of , then general solution of the non-homogenous differential equation is image, where image is the complementary solution and image is the particular solution.

General solution of the complementary equation:

If the differential equation is in the form of , then general solution of the complementary equation is image

Particular solution of the differential equation :

If the differential equation is in the form of then the particular solution of the equation is , where

and .

Here is the wronskian of and .

.

Step 2:

Consider the auxiliary equation of the differential equation.

Since the roots of the equation are real and distinct then the solution of the differential equation is .

The particular solution of the differential equation is in the form of , where and .

Find wronskian of and is

answered Feb 25, 2015 by Lucy Mentor
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Contd...

Step 3:

Find image.

image

Re-write the expression.

image

Find image.

image

Re-write the expression.

image

Step 4:

Substitute the values of , , image and image in .

image.

General solution of the differential equation is image.

image

Solution of the differential equation is image.

Solution:

Solution of the differential equation is image.

answered Feb 25, 2015 by Lucy Mentor

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