29.23.12 problem 643

Internal problem ID [5234]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 643
Date solved : Monday, January 27, 2025 at 10:37:20 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} x \left (2 x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 37

dsolve(x*(2*x^2+y(x)^2)*diff(y(x),x) = (2*x^2+3*y(x)^2)*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{2 c_{1}} \sqrt {2}\, \sqrt {\frac {{\mathrm e}^{-4 c_{1}}}{x^{4} \operatorname {LambertW}\left (\frac {2 \,{\mathrm e}^{-4 c_{1}}}{x^{4}}\right )}}\, x^{3} \]

✓ Solution by Mathematica

Time used: 7.229 (sec). Leaf size: 65

DSolve[x(2 x^2+y[x]^2)D[y[x],x]==(2 x^2+3 y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {2} x}{\sqrt {W\left (\frac {2 e^{-3-2 c_1}}{x^4}\right )}} \\ y(x)\to \frac {\sqrt {2} x}{\sqrt {W\left (\frac {2 e^{-3-2 c_1}}{x^4}\right )}} \\ y(x)\to 0 \\ \end{align*}