Internal problem ID [3004]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 256.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}+2 x \left (1-x \right ) y-{\mathrm e}^{x} \left (-1+2 \,{\mathrm e}^{x}\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(x^2*diff(y(x),x)+2*x*(1-x)*y(x) = exp(x)*(2*exp(x)-1),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (2 x +{\mathrm e}^{-x}+c_{1}\right ) {\mathrm e}^{2 x}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.071 (sec). Leaf size: 24
DSolve[x^2 y'[x]+2 x(1-x)y[x]==Exp[x](2 Exp[x]-1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^x \left (1+e^x (2 x+c_1)\right )}{x^2} \\ \end{align*}