Find the solution of the given initial value problem in explicit form.
y' = (1-11x)y^2, y(0) = -1/8

Question

Find the solution of the given initial value problem in explicit form.
y' = (1-11x)y^2, y(0) = -1/8

anonymous · Answer

this is saperable

zepdrix · Answer

$$\Large\bf\sf y'\quad=\quad (1-11x)y^2$$Hmm so this appears to be separable.$$\Large\bf\sf \frac{dy}{y^2}\quad=\quad (1-11x)dx$$From here we integrate.
Understand that much of it?

anonymous · Answer

oh ok i got -y^-1 = x-(11/2)^2 is that right?

zepdrix · Answer

(11/2)x^2?

Mmm ya looks good!
Don't forget a constant of integration somewhere$$\Large\bf\sf -\frac{1}{y}\quad=\quad x-\frac{11}{2}x^2+c$$

zepdrix · Answer

So we need to solve for y as our next step.

zepdrix · Answer

err actually, let's use the initial data before solving for y explicitly.
It'll be easier from here I think.

zepdrix · Answer

$$\Large\bf\sf y(0)=-\frac{1}{8}$$Plugging this in:$$\Large\bf\sf 8\quad=\quad 0-\frac{11}{2}0^2+c$$Understand how that left side simplified?

anonymous · Answer

hmmm... how did -1/y become 8?

anonymous · Answer

ohhh never mind i got it.