Question

If dy/dx = e^x/y^2 and y(0) =1, find an equation for y in terms of x

Answer 1

These are separable variables. Move the dx to the right, and the y^2 to the left, integrate both sides, and simplify to put the equation into y(x) form.

Answer 2

yep..Separable Differential equation...my ans was y=((3(e^x) -2/3))^1/3..

Answer 3

After considering the initial condition, I got\[y(x) = 3^{1/3}*e^{x/3}+1-3^{1/3} = 1+3^{1/3}*(e^{x/3}-1)\]