Internal problem ID [6180]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime } x -2 y x^{2}-\ln \left (x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)=2*x^2*y(x)+y(x)*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {\ln \left (x \right )^{2}}{2}+x^{2}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 27
DSolve[x*y'[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*}