29.9.16 problem 256

Internal problem ID [4856]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 9
Problem number : 256
Date solved : Monday, January 27, 2025 at 09:42:51 AM
CAS classification : [_linear]

\begin{align*} x^{2} y^{\prime }+2 x \left (1-x \right ) y&={\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.001 (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)
 

\[ y \left (x \right ) = \frac {\left (2 x +c_{1} \right ) {\mathrm e}^{2 x}+{\mathrm e}^{x}}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 24

DSolve[x^2 D[y[x],x]+2 x(1-x)y[x]==Exp[x](2 Exp[x]-1),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x \left (1+e^x (2 x+c_1)\right )}{x^2} \]