So I am given the problem: y'= (t+y)^2(y^2)+ sin(y^3) +ye^(ty), y(0) = 0   This initial value problem satisfies the existence and uniqueness theorem criteria using interval (−∞,∞) for both the t and y variables, and hence has a unique solution. Find this unique solution.   I found out that y'(0) = 0 given the initial condition. Where do I go from here?

Question

So I am given the problem:

y'= (t+y)^2(y^2)+ sin(y^3) +ye^(ty), y(0) = 0
 
This initial value problem satisfies the existence and uniqueness theorem criteria using
interval (−∞,∞) for both the t and y variables, and hence has a unique solution. Find
this unique solution.
 
I found out that y'(0) = 0 given the initial condition. Where do I go from here?

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