Internal problem ID [3065]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 11
Problem number: 317.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {x \left (x +1\right ) y^{\prime }-\left (x +1\right ) \left (x^{2}-1\right )-\left (x^{2}+x -1\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(x*(1+x)*diff(y(x),x) = (1+x)*(x^2-1)+(x^2+x-1)*y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{x} \left (x +1\right ) c_{1}}{x}-x -1 \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 22
DSolve[x(1+x)y'[x]==(x+1)(x^2-1)+(x^2+x-1)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(x+1) \left (-x+c_1 e^x\right )}{x} \\ \end{align*}