15.4.21 problem 22

Internal problem ID [2934]
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
Date solved : Monday, January 27, 2025 at 06:58:50 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, _dAlembert]

\begin{align*} \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 \end{align*}

✓ Solution by Maple

Time used: 0.420 (sec). Leaf size: 73

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)
 

\[ y = \operatorname {RootOf}\left (x^{3} {\mathrm e}^{3 c_1} \textit {\_Z}^{24}-4 \textit {\_Z}^{15}-3 x^{3} {\mathrm e}^{3 c_1}\right )^{5} \sqrt {\frac {\operatorname {RootOf}\left (x^{3} {\mathrm e}^{3 c_1} \textit {\_Z}^{24}-4 \textit {\_Z}^{15}-3 x^{3} {\mathrm e}^{3 c_1}\right )^{5}}{x}}\, {\mathrm e}^{-\frac {3 c_1}{2}} \]

✓ Solution by Mathematica

Time used: 60.157 (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))*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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