29.6.4 problem 150

Internal problem ID [4750]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 6
Problem number : 150
Date solved : Monday, January 27, 2025 at 09:36:22 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }&=x^{n} \ln \left (x \right )-y \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 34

dsolve(x*diff(y(x),x) = x^n*ln(x)-y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (-1+\left (n +1\right ) \ln \left (x \right )\right ) x \,x^{n}+c_{1} \left (n +1\right )^{2}}{\left (n +1\right )^{2} x} \]

✓ Solution by Mathematica

Time used: 0.089 (sec). Leaf size: 29

DSolve[x D[y[x],x]==x^n Log[x]-y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^n ((n+1) \log (x)-1)}{(n+1)^2}+\frac {c_1}{x} \]