Question

Solve:

$\frac{dy}{dx}=y^2$ with $y\left(1\right)=1$.

Answer 1

Given the differential equation is,

$\frac{dy}{dx}=y^2$

$\frac{dy}{y^2}=dx$

Now integrating both sides we get,

$-\frac{1}{y}=x+c$.

Also given $y\left(1\right)=1$

$-1=1+c$

$c=2$.

So the solution of the given differential equation is $-\frac{1}{y}=x-2$ or, $y=\frac{1}{2-x}$ for $x\ne 2$.