Find the first four nonzero terms in a power series expansion of the solution to the given initial value problem

Question

5y'-3e^xy=0; y(0)=3

(Type an expression that includes all terms up to order 3.)

Answer 1

Starting with y' = (3/5)e^xy = 0 with y(0) = 3

I obtain

y'(0) = 9/5, y''(0) = 72/75, y'''(0) = 711/125

So, using Taylor's Equation

y = f(x) = 3 + 9x/5 + 36x²/75 + 711x³/750........