Internal problem ID [5417]
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: 2(d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {y}{x}-x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 12
dsolve([diff(y(x),x)-y(x)/x=x^2,y(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x^{2}+5\right ) x}{2} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 15
DSolve[{y'[x]-y[x]/x==x^2,{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x \left (x^2+5\right ) \\ \end{align*}