29.22.19 problem 627

Internal problem ID [5219]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 22
Problem number : 627
Date solved : Monday, January 27, 2025 at 10:22:52 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} \left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve((2*x^2+3*y(x)^2)*diff(y(x),x)+x*(3*x+y(x)) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \operatorname {RootOf}\left (\int _{}^{\textit {\_Z}}\frac {3 \textit {\_a}^{2}+2}{\textit {\_a}^{3}+\textit {\_a} +1}d \textit {\_a} +3 \ln \left (x \right )+3 c_{1} \right ) x \]

✓ Solution by Mathematica

Time used: 0.153 (sec). Leaf size: 66

DSolve[(2*x^2+3*y[x]^2)*D[y[x],x]+x*(3*x+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}+1\&,\frac {3 \text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2+1}\&\right ]=-3 \log (x)+c_1,y(x)\right ] \]