Thread: Another DE initial value problem

Suppose that y=y(x) is a solution of the initial value problem
y' + e^x y = x^2, y(0) = 4
Find y'(0) , y''(0)

So how am I suppose to do the question? I started by doing the integrating factor method but ended up with e^(e^x). So am I on the right track? If not, can someone be kind enough to show me the right way. Many thanks xD

Originally Posted by b4byp4nd4

Suppose that y=y(x) is a solution of the initial value problem
y' + e^x y = x^2, y(0) = 4
Find y'(0) , y''(0)

So how am I suppose to do the question? I started by doing the integrating factor method but ended up with e^(e^x). So am I on the right track? If not, can someone be kind enough to show me the right way. Many thanks xD

Substitute y = 4 when x = 0 into the given DE: y'(0) + e^0 (4) = 0^2 => y'(0) = -4.

Now differentiate the DE: y'' + e^x y + e^x y' = 2x.

Substitute y'(0) = -4 and y(0) = 4 and solve for y''.