Internal problem ID [3367]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 22
Problem number: 627.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _dAlembert]
Solve \begin {gather*} \boxed {\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \relax (x ) = \RootOf \left (\int _{}^{\textit {\_Z}}\frac {3 \textit {\_a}^{2}+2}{\textit {\_a}^{3}+\textit {\_a} +1}d \textit {\_a} +3 \ln \relax (x )+3 c_{1}\right ) x \]
✓ Solution by Mathematica
Time used: 0.14 (sec). Leaf size: 66
DSolve[(2 x^2+3 y[x]^2)y'[x]+x(3 x+y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^3+\text {$\#$1}+1\&,\frac {3 \text {$\#$1}^2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )+2 \log \left (\frac {y(x)}{x}-\text {$\#$1}\right )}{3 \text {$\#$1}^2+1}\&\right ]=-3 \log (x)+c_1,y(x)\right ] \]