Trouble with particular solution of differential equation - rewrite my answer?

[cowmoo32]

Trouble with particular solution of differential equation - [SOLVED]

Homework Statement

Find the particular solution of the differential equation

satisfying the initial condition

The Attempt at a Solution

[STRIKE]I end up with (1/2)ln(-x^2+10x) which does satisfy the initial conditions, yet it's coming back as incorrect. Is there another way I can write the formula?[/STRIKE]

I figured it out, check post #3

 

[Mark44]

Homework Statement

Find the particular solution of the differential equation

satisfying the initial condition

The Attempt at a Solution

I end up with (1/2)ln(-x^2+10x) which does satisfy the initial conditions, yet it's coming back as incorrect. Is there another way I can write the formula?

Show how you got the result you show. I assume you mean y = (1/2)ln(-x² + 10x).

Satisfying the initial conditions is not enough: the solution has to satisfy the differential equation, too.

 

[cowmoo32]

Scratch that above, I had a negative out of place. See below. I corrected it and it's coming back as correct.

\frac{dy}{dx}=e^-2x(x-5)

\int (e^2y)dy = \int (x-5)dx

e^2y = x² - 10x + C

2y = ln(x² - 10x + C)

C = 50