19.2.12 problem 12

Internal problem ID [3541]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.6, page 50
Problem number : 12
Date solved : Monday, January 27, 2025 at 07:41:11 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve(diff(y(x),x)-y(x)/x=2*x^2*ln(x),y(x), singsol=all)
 

\[ y \left (x \right ) = x^{3} \ln \left (x \right )-\frac {x^{3}}{2}+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 23

DSolve[D[y[x],x]-y[x]/x==2*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^3}{2}+x^3 \log (x)+c_1 x \]