7.5.12 problem 12

Internal problem ID [116]
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 1.6 (substitution and exact equations). Problems at page 72
Problem number : 12
Date solved : Friday, February 07, 2025 at 07:51:21 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

dsolve(x*y(x)*diff(y(x),x)=y(x)^2+x*sqrt(4*x^2+y(x)^2),y(x), singsol=all)
 

\[ \frac {\ln \left (x \right ) x -c_1 x -\sqrt {4 x^{2}+y^{2}}}{x} = 0 \]

✓ Solution by Mathematica

Time used: 0.293 (sec). Leaf size: 54

DSolve[x*y[x]*D[y[x],x]==y[x]^2+x*Sqrt[4*x^2+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
 

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