Use method of variation of parameters to solve y'' + y = sin^2(x)

Use method of variation of parameters to solve

y'' + y = sin^2(x)

Expert Solution

The given differential equation is

And the homogeneous part of the equation is given by

This is a 2nd order differential equation, so, it must have two linearly independent solutions.
And the linearly independent solutions of the homogeneous part of the equation are

And so, the Wronskian of these two Linearly independent solutions is

So, we have


And if we choose the particular solution

then,

where,

So, putting the values, we get


So, the particular solution is


So, the general solution is

where, c1 and c2 are constants.

genius_generous answered 2 years ago

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