Internal problem ID [14248]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-y x=x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 14
dsolve(diff(y(x),x)-y(x)*x=x,y(x), singsol=all)
\[ y \left (x \right ) = -1+c_{1} {\mathrm e}^{\frac {x^{2}}{2}} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 24
DSolve[y'[x]-y[x]*x==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+c_1 e^{\frac {x^2}{2}} \\ y(x)\to -1 \\ \end{align*}