What's the General Solution to This IVP?

[logan3]

$\frac {dy}{dt} = y^3 + t^2, y(0) = 0$

My teacher said this IVP couldn't be expressed in terms of functions we commonly know. I was wondering what the general solution is?

Thank-you

 

[Raghav Gupta]

$\frac {dy}{dt} = y^3 + t^2, y(0) = 0$

My teacher said this IVP couldn't be expressed in terms of functions we commonly know. I was wondering what the general solution is?

Thank-you

For solving this
It is a bernoulli form
Watch this video and you will get it how to solve

 

[LCKurtz]

$\frac {dy}{dt} = y^3 + t^2, y(0) = 0$ is not of the form $y' + f(t)y = g(t)y^n$ so it is not the Bernoulli equation.

 

[Raghav Gupta]

Yes it's not Bernoulli form, sorry. I not know how to solve it, but Wolframalpha was showing the simple answer x=1 for y=0.
I don't know how it solved that.