Internal problem ID [5415]
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(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }-2 x y-6 \,{\mathrm e}^{x^{2}} x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 18
dsolve([diff(y(x),x)-2*x*y(x)=6*x*exp(x^2),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \left (3 x^{2}-3+{\mathrm e}^{-1}\right ) {\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 23
DSolve[{y'[x]-2*x*y[x]==6*x*Exp[x^2],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^2-1} \left (3 e \left (x^2-1\right )+1\right ) \\ \end{align*}