Solve the Initial Value problem

[lmanri]

dy/dt=t^(2)y^(3) , y(0)=-1

I need help solving this

I put the integral (dy/y^3)= integral (t^2)dt
but idk what to do after that or if that's even right

 

[ehild]

Hi Imanri,

You dropped an integral sign...

$$\int{\frac{dy}{y^3}}=\int{t^2dt}$$

Do the integration on both sides.

ehild

 

[lmanri]

Thank you, but after I find that what do I do with y(0)=1

 

[ehild]

You have an undetermined constant after integration. Substitute t=0 and y=-1 in your integral and solve for c.

ehild

 

[lmanri]

Thank you

 

[ehild]

What is your solution?

ehild

 

[lmanri]

y=-1/(t^(3)+C)