15.4.23 problem 24

Internal problem ID [2936]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 8, page 34
Problem number : 24
Date solved : Monday, January 27, 2025 at 06:59:39 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 39

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

\begin{align*} y &= \sqrt {-x^{2}+{\mathrm e}^{-\frac {c_1}{x}}} \\ y &= -\sqrt {-x^{2}+{\mathrm e}^{-\frac {c_1}{x}}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.945 (sec). Leaf size: 47

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

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