50.3.12 problem 2(b)

Internal problem ID [7836]
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)
Date solved : Monday, January 27, 2025 at 03:24:27 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-2 y x&=6 x \,{\mathrm e}^{x^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.034 (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)
 

\[ y = \left (3 x^{2}-3+{\mathrm e}^{-1}\right ) {\mathrm e}^{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 23

DSolve[{D[y[x],x]-2*x*y[x]==6*x*Exp[x^2],{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^2-1} \left (3 e \left (x^2-1\right )+1\right ) \]