Internal problem ID [17]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.3. Slope fields and solution curves. Page 26
Problem number: 8.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-x^{2}+y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 18
dsolve(diff(y(x),x) = x^2-y(x),y(x), singsol=all)
\[ y \relax (x ) = x^{2}-2 x +2+{\mathrm e}^{-x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 20
DSolve[y'[x] == x^2-y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-2) x+c_1 e^{-x}+2 \\ \end{align*}