44.4.36 problem 17

Internal problem ID [7049]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:42:27 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

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

\[ y = \frac {x^{2}}{2}-\frac {x}{2}+\frac {1}{4}+c_{1} {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 28

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

\[ y(x)\to \frac {1}{4} \left (2 x^2-2 x+1\right )+c_1 e^{-2 x} \]