Internal problem ID [5662]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of
First-Order Differential Equations Page 162
Problem number: 1(f) solving directly.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-y-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 18
dsolve(diff(y(x),x)-y(x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = -x^{2}-2 x -2+c_{1} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 19
DSolve[y'[x]-y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x (x+2)+c_1 e^x-2 \\ \end{align*}