50.3.24 problem 6

Internal problem ID [7848]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 6
Date solved : Monday, January 27, 2025 at 03:25:42 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 27

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

\begin{align*} y(x)\to c_1 e^{x^2+\frac {\log ^2(x)}{2}} \\ y(x)\to 0 \\ \end{align*}