Question

Solve this Linear DE: y'+3x^2y=x^2

need a check at the end

Answer 1

\[e^{\int{}{}p(x)dx}=e^{\int{}{}3x^2}=e^{x^3}\]

Answer 2

\[\frac{d}{dx}e^{x^3}y=e^{x^3}x^2\]

Answer 3

\[e^{x^3}y=\int{}{}e^{x^3}x^2dx\]

Answer 4

u=x^3
du=3x^2dx
du/3=x^2dx

Answer 5

\[e^{x^3}y=\frac{1}{3}\int{}{}e^udu\]

Answer 6

\[e^{x^3}y=\frac{1}{3}e^{u}+\frac{1}{3}c=\frac{e^{x^3}}{3}+\frac{c}{3}\]

Answer 7

c/3 = c

Answer 8

\[y=\frac{1}{3}+ce^{-x^3}\]

Answer 9

I chcked it was correct

Answer 10

looks right to me