Internal problem ID [3416]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 160.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {x y^{\prime }-\left (-2 x^{2}+1\right ) y=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x) = x^3+(-2*x^2+1)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{2}+x \,{\mathrm e}^{-x^{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 21
DSolve[x y'[x]==x^3+(1-2 x^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x \left (\frac {1}{2}+c_1 e^{-x^2}\right ) \]