29.1.9 problem 8

Internal problem ID [4616]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 1
Problem number : 8
Date solved : Monday, January 27, 2025 at 09:26:22 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=x \left ({\mathrm e}^{-x^{2}}+a y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

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

\[ y \left (x \right ) = \frac {{\mathrm e}^{\frac {a \,x^{2}}{2}} \left (-{\mathrm e}^{-\frac {x^{2} \left (2+a \right )}{2}}+c_{1} \left (2+a \right )\right )}{2+a} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 42

DSolve[D[y[x],x]==x*(Exp[-x^2]+a*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{\frac {a x^2}{2}} \left (-e^{-\frac {1}{2} (a+2) x^2}+(a+2) c_1\right )}{a+2} \]