74.1.53 problem 73

Internal problem ID [15833]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 73
Date solved : Tuesday, January 28, 2025 at 08:08:33 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 23

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

\begin{align*} y(x)\to -\frac {x^2}{x-c_1} \\ y(x)\to 0 \\ \end{align*}