78.6.8 problem 2 (h)

Internal problem ID [18176]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 2 (h)
Date solved : Tuesday, January 28, 2025 at 11:36:16 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(diff(y(x),x)-2*x*y(x)=6*x*exp(x^2),y(x), singsol=all)
 

\[ y = \left (3 x^{2}+c_1 \right ) {\mathrm e}^{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 19

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

\[ y(x)\to e^{x^2} \left (3 x^2+c_1\right ) \]