7.2.7 problem 8

Internal problem ID [25]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.3. Problems at page 27
Problem number : 8
Date solved : Friday, February 07, 2025 at 08:12:07 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)
 

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

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 21

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

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