Internal problem ID [10153]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 18.
Transformation of variables. Page 26
Problem number: Ex 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime } x -y+2 x^{2} y-x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)-y(x)+2*x^2*y(x)-x^3=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{2}+x \,{\mathrm e}^{-x^{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 21
DSolve[x*y'[x]-y[x]+2*x^2*y[x]-x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \left (\frac {1}{2}+c_1 e^{-x^2}\right ) \\ \end{align*}