29.11.26 problem 317

Internal problem ID [4917]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 317
Date solved : Monday, January 27, 2025 at 09:50:32 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (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)
 

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

✓ Solution by Mathematica

Time used: 0.077 (sec). Leaf size: 22

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

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