20.3.26 problem Problem 33

Internal problem ID [3635]
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 33
Date solved : Monday, January 27, 2025 at 07:48:03 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 17

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

\[ y(x)\to x (-x+x \log (x)+c_1) \]