29.24.32 problem 695

Internal problem ID [5285]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 24
Problem number : 695
Date solved : Monday, January 27, 2025 at 11:04:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 27

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

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{3 \textit {\_Z}}+9 \,{\mathrm e}^{\textit {\_Z}}+3 c_{1} +3 \textit {\_Z} +3 \ln \left (x \right )\right )} x \]

✓ Solution by Mathematica

Time used: 0.151 (sec). Leaf size: 37

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

\[ \text {Solve}\left [\frac {y(x)^3}{3 x^3}+\frac {3 y(x)}{x}+\log \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]