20.4.15 problem Problem 23

Internal problem ID [3650]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 23
Date solved : Monday, January 27, 2025 at 07:50:08 AM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

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

\[ \frac {x \ln \left (x \right )-c_{1} x -\sqrt {x^{2}+y \left (x \right )^{2}}}{x} = 0 \]

✓ Solution by Mathematica

Time used: 0.290 (sec). Leaf size: 54

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

\begin{align*} y(x)\to -x \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} \\ y(x)\to x \sqrt {\log ^2(x)+2 c_1 \log (x)-1+c_1{}^2} \\ \end{align*}