# Math Help - separable differential equation

1. ## separable differential equation

In the above I get y^3+y = x^2 +5x +c

but then if it passes through (1,0) then when x=1, y =0. That gives me 0=7 so I must have gone wrong somewhere. I'm not sure what I'm doing wrong here.

thanks

MH

2. ## Re: separable differential equation

$\dfrac {dy}{dx}=\dfrac{4x+5}{3y^2+1}$

$(3y^2+1)~dy = (4x+5)~dx$

$y^3+y = 2x^2 + 5x + C$

we need to find $C$ to satisfy the constraint that the curve passes through $(1,0)$

$0=2(1^2) + 5(1) + C$

$0=2 + 5 + C$

$C=-7$

The implicit form of your curve is thus

$y^3+y=2x^2+5x-7$

This will have an explicit form for $y$ in terms of $x$ but it will be a mess. The implicit form should suffice.

3. ## Re: separable differential equation

OH thanks much!