Internal problem ID [5414]
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(a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-y x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3] \end {align*}
✓ Solution by Maple
Time used: 7.828 (sec). Leaf size: 14
dsolve([diff(y(x),x)-x*y(x)=0,y(1) = 3],y(x), singsol=all)
\[ y \relax (x ) = 3 \,{\mathrm e}^{\frac {\left (x -1\right ) \left (x +1\right )}{2}} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 18
DSolve[{y'[x]-x*y[x]==0,{y[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 3 e^{\frac {1}{2} \left (x^2-1\right )} \\ \end{align*}