Internal problem ID [13360]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page
103
Problem number: 5.2 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-2 y x=x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve(diff(y(x),x)-2*x*y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{2}+{\mathrm e}^{x^{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 24
DSolve[y'[x]-2*x*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2}+c_1 e^{x^2} \\ y(x)\to -\frac {1}{2} \\ \end{align*}