Internal problem ID [6168]
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]
\[ \boxed {-2 y x +y^{\prime }=6 \,{\mathrm e}^{x^{2}} x} \] With initial conditions \begin {align*} [y \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.032 (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)
\[ y \left (x \right ) = \left (3 x^{2}-3+{\mathrm e}^{-1}\right ) {\mathrm e}^{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 23
DSolve[{y'[x]-2*x*y[x]==6*x*Exp[x^2],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{x^2-1} \left (3 e \left (x^2-1\right )+1\right ) \]