Internal problem ID [3418]
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]
\[ \boxed {x y^{\prime }+\left (-x^{2} a +2\right ) y=-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(x*diff(y(x),x)+x+(-a*x^2+2)*y(x) = 0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\frac {{\mathrm e}^{-\frac {a \,x^{2}}{2}} x}{a}-\frac {\sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, \sqrt {a}\, x}{2}\right )}{2 a^{\frac {3}{2}}}+c_{1} \right ) {\mathrm e}^{\frac {a \,x^{2}}{2}}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 70
DSolve[x y'[x]+x+(2-a x^2)y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-\frac {\sqrt {2 \pi } e^{\frac {a x^2}{2}} \text {erf}\left (\frac {\sqrt {a} x}{\sqrt {2}}\right )}{a^{3/2}}+2 c_1 e^{\frac {a x^2}{2}}+\frac {2 x}{a}}{2 x^2} \]