Internal problem ID [2898]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 150.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -x^{n} \ln \relax (x )+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 36
dsolve(x*diff(y(x),x) = x^n*ln(x)-y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{n} \ln \relax (x )}{n +1}-\frac {x^{n}}{n^{2}+2 n +1}+\frac {c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.083 (sec). Leaf size: 29
DSolve[x y'[x]==x^n Log[x]-y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^n ((n+1) \log (x)-1)}{(n+1)^2}+\frac {c_1}{x} \\ \end{align*}