Something wrong? can't find my error.

[shseo0315]

Homework Statement

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

Homework Equations

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.

please help. I can't find what went wrong.

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

help~~

 

[Mark44]

Homework Statement

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

Homework Equations

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.

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.

please help. I can't find what went wrong.

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

help~~

 

[Office_Shredder]

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

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