Seperation of variable differential

[ahhgidaa]

Homework Statement

2y dy/dx = xy^2 + x

y(0)= 2

The Attempt at a Solution

the first step i did was take out the x on the right for x(y^2+1)

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

then shift things around

2y/(y^2+1) dy = x dx
then integrate
u substitution gives

ln y^2+1 = 1/2 x^2 + C

turn e^c into A

y^2+1 = A e^ 1/2 x^2

now my algebra and other stuff gets rusty and dnt know if I am right

y= sqrt ( A e^(1/2x^2) - 1

with y(0) = 2 i multiply the A and (e^0) 1 first right? then subtract 1 . so A=5?
.x=0 y=2.

so would the final answer be y=sqrt(5e^(1/2x^2)+1)

i got a = 4 the first time but thought my math was wrong.

 

[SammyS]

Yes, A = 5.

So, y = sqrt{5e^(x²/2) - 1}

You changed the sign on the 1 when you wrote your final result.