Internal problem ID [2482]
Book: Differential equations, Shepley L. Ross, 1964
Section: 2.4, page 55
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 23
dsolve((4*x*y(x)^2+6*y(x))+(5*x^2*y(x)+8*x)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\RootOf \left (-\ln \relax (x )+c_{1}+\ln \left (2+\textit {\_Z} \right )+4 \ln \left (\textit {\_Z} \right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 1.951 (sec). Leaf size: 156
DSolve[(4*x*y[x]^2+6*y[x])+(5*x^2*y[x]+8*x)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Root}\left [-\text {$\#$1}^5-\frac {2 \text {$\#$1}^4}{x}+\frac {e^{c_1}}{x^4}\&,1\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^5-\frac {2 \text {$\#$1}^4}{x}+\frac {e^{c_1}}{x^4}\&,2\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^5-\frac {2 \text {$\#$1}^4}{x}+\frac {e^{c_1}}{x^4}\&,3\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^5-\frac {2 \text {$\#$1}^4}{x}+\frac {e^{c_1}}{x^4}\&,4\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^5-\frac {2 \text {$\#$1}^4}{x}+\frac {e^{c_1}}{x^4}\&,5\right ] \\ \end{align*}