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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.