15.4.22 problem 23

Internal problem ID [2935]
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 : 23
Date solved : Monday, January 27, 2025 at 06:59:11 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 3.373 (sec). Leaf size: 33

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

\[ y = \frac {c_1 \operatorname {RootOf}\left (\textit {\_Z}^{16} c_1^{2}+2 x^{4} \textit {\_Z}^{4}-x^{4}\right )^{6}}{x} \]

✓ Solution by Mathematica

Time used: 60.308 (sec). Leaf size: 3381

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

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