44.2.24 problem 24

Internal problem ID [6956]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 24
Date solved : Monday, January 27, 2025 at 02:38:24 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y-x \right ) y^{\prime }&=x +y \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 49

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

\begin{align*} y &= \frac {c_{1} x -\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y &= \frac {c_{1} x +\sqrt {2 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.435 (sec). Leaf size: 86

DSolve[(y[x]-x)*D[y[x],x]==y[x]+x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x-\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to x+\sqrt {2 x^2+e^{2 c_1}} \\ y(x)\to x-\sqrt {2} \sqrt {x^2} \\ y(x)\to \sqrt {2} \sqrt {x^2}+x \\ \end{align*}