Internal problem ID [11703]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page
67
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {4 y^{2} x +6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.078 (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)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +\ln \left (\textit {\_Z} +2\right )+4 \ln \left (\textit {\_Z} \right )\right )}{x} \]
✓ Solution by Mathematica
Time used: 1.767 (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*}