29.23.21 problem 652

Internal problem ID [5243]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 23
Problem number : 652
Date solved : Monday, January 27, 2025 at 10:43:46 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.082 (sec). Leaf size: 21

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

\[ y \left (x \right ) = {\mathrm e}^{\operatorname {RootOf}\left ({\mathrm e}^{2 \textit {\_Z}}+a \,{\mathrm e}^{\textit {\_Z}}+c_{1} +\textit {\_Z} +\ln \left (x \right )\right )} x \]

✓ Solution by Mathematica

Time used: 0.171 (sec). Leaf size: 34

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

\[ \text {Solve}\left [\frac {a y(x)}{x}+\frac {y(x)^2}{x^2}+\log \left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]