Internal problem ID [1963]
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: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _exact, _rational, _dAlembert]
\[ \boxed {\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )}=0} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 45
dsolve((x^2+3*y(x)^2)/(x*(3*x^2+4*y(x)^2))+(2*x^2+y(x)^2)/(y(x)*(3*x^2+4*y(x)^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = {\left (\frac {\operatorname {RootOf}\left (x^{3} {\mathrm e}^{3 c_{1}} \textit {\_Z}^{24}-4 \textit {\_Z}^{15}-3 x^{3} {\mathrm e}^{3 c_{1}}\right )^{5}}{x}\right )}^{\frac {3}{2}} {\mathrm e}^{-\frac {3 c_{1}}{2}} x \]
✓ Solution by Mathematica
Time used: 60.136 (sec). Leaf size: 1649
DSolve[(x^2+3*y[x]^2)/(x*(3*x^2+4*y[x]^2))+(2*x^2+y[x]^2)/(y[x]*(3*x^2+4*y[x]^2))*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
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