Saved Bookmarks
| 1. |
\( \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=\frac{1}{1+e^{x}} \) |
|
Answer» Given differential equation is \(\frac{d^2y}{dx^2}+\frac{dy}{dx}=\frac{1}{1+e^x}\)\(=\frac{e^{-x}}{e^{-x}(1+e^x)}=\frac{e^{-x}}{e^{-x}+1}\) ⇒ \(\int\frac{d^2y}{dx^2}dx+\int\frac{dy}{dx}dx\) = \(\int\frac{e^{-x}}{e^{-x}+1}dx\)(By taking integration w.r.t. x) ⇒ \(\frac{dy}{dx}+y = -log(e^{-x}+1)\) which is solution of given differential equation. |
|