# Homework Help: Something wrong? can't find my error.

1. Sep 1, 2010

### shseo0315

1. The problem statement, all variables and given/known data

x dy/dx -y = 2x^2 y, y(1)=1

2. Relevant equations

3. The attempt at a solution

x dy/dx = y(2x^2 + 1)

int 1/y dy = int (2x^2+1)/x dx

int 1/y dy = int 2x dx + int 1/x dx

ln y = x^2 + lnx + c

y = exp(x^2 + c) + x and in this case initial condition doesn't work.

The answer turns out to be y = x exp(x^2-1).

help~~

2. Sep 1, 2010

### Staff: Mentor

Your error is in the line above. Since lny = x^2 + lnx + C, then y = e^(lnx + x^2 + C). Now think about the laws of exponents, particularly that a^(m + n) = a^m * a^n.

3. Sep 1, 2010

### Office_Shredder

Staff Emeritus
$$e^{x^2+lnx+c}=e^{x^2}e^{lnx}e^c=xe^{x^2}e^c$$

You seem to have confused multiplication and addition for your last step