8.2.7 problem 8

Internal problem ID [667]
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
Date solved : Monday, January 27, 2025 at 02:56:59 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }&=x^{2}-y \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 18

dsolve(diff(y(x),x) = x^2-y(x),y(x), singsol=all)
 

\[ y = x^{2}-2 x +2+{\mathrm e}^{-x} c_1 \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 21

DSolve[D[y[x],x] == x^2-y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2-2 x+c_1 e^{-x}+2 \]