20.3.13 problem Problem 13

Internal problem ID [3622]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 13
Date solved : Monday, January 27, 2025 at 07:47:44 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: 0.001 (sec). Leaf size: 19

dsolve(diff(y(x),x)-1/x*y(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: 0.033 (sec). Leaf size: 23

DSolve[D[y[x],x]-1/x*y[x]==2*x^2*Log[x],y[x],x,IncludeSingularSolutions -> True]
 

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