Internal problem ID [2910]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 162.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x +x +\left (-a \,x^{2}+2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 50
dsolve(x*diff(y(x),x)+x+(-a*x^2+2)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\frac {{\mathrm e}^{-\frac {a \,x^{2}}{2}} x}{a}-\frac {\sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {\sqrt {2}\, \sqrt {a}\, x}{2}\right )}{2 a^{\frac {3}{2}}}+c_{1}\right ) {\mathrm e}^{\frac {a \,x^{2}}{2}}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 69
DSolve[x y'[x]+x+(2-a x^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 \sqrt {a} x+e^{\frac {a x^2}{2}} \left (-\sqrt {2 \pi } \text {Erf}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )+2 a^{3/2} c_1\right )}{2 a^{3/2} x^2} \\ \end{align*}