Question

(1+x^2)dy/DX + (1-x^2)y = xe^-x(1+x^2). please solve this problem​​

Answer 1

hi this is the answer i think

Answer 2

Answer:

$\mathrm{\left(1+x^2\right)\frac{dy}{dx}+\left(1-x^2\right)y=xe^{-x}\left(1+x^2\right):\quad y=\frac{\int \:e^{-2x+2\arctan \left(x\right)}xdx}{e^{2\arctan \left(x\right)-x}}}$

Step-by-step explanation:

$\mathrm{\left(1+x^2\right)\frac{dy}{dx}+\left(1-x^2\right)y=xe^{-x}\left(1+x^2\right)}$

$\mathrm{Substitute\:\frac{dy}{dx}}\mathrm{\:with\:}y'\:$

$\mathrm{\left(1+x^2\right)y'\:+\left(1-x^2\right)y=xe^{-x}\left(1+x^2\right)}$

$\mathrm{y'\:+\frac{1-x^2}{1+x^2}y=e^{-x}x}$

$\mathrm{y=\frac{\int \:e^{-2x+2\arctan \left(x\right)}xdx}{e^{2\arctan \left(x\right)-x}}}$