44.1.20 problem 22

Internal problem ID [6895]
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. Exercises 1.1 at page 12
Problem number : 22
Date solved : Monday, January 27, 2025 at 02:34:18 PM
CAS classification : [[_homogeneous, `class G`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.083 (sec). Leaf size: 31

dsolve(2*x*y(x)+(x^2-y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= x^{2}-\sqrt {x^{4}+c_{1}} \\ y &= x^{2}+\sqrt {x^{4}+c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.118 (sec). Leaf size: 58

DSolve[2*x*y[x]+(x^2-y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^2-i \sqrt {-x^4-c_1} \\ y(x)\to x^2+i \sqrt {-x^4-c_1} \\ y(x)\to 0 \\ \end{align*}