Originally Posted by

**pberardi** Hello,

I have this diffyQ problem that asks to find the solution that passes through a specific point. I have worked it out to where I have a ( i think correct ) equation for y, but am not sure how to deal with the constant and make sure it passes through a specific point.

Solve: Find the solution of y' = 2(2x-y) that passes through the point P(0,1).

Solution:

y' = 4x -2y

y' + 2y = 4x

integrating factor is e^(2x)

d/dx of [e^(2x)y] = 4xe^(2x)

integrate both sides

RHS by parts gives

2xe^(2x) - e^2x

So:

e^(2x)y = 2xe^(2x) - e^(2x) + C

y = 2x - 1 + Ce^(-2x)

Could someone check this out