Internal problem ID [11704]
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: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {8 y^{3} x^{2}-2 y^{4}+\left (5 y^{2} x^{3}-8 y^{3} x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.703 (sec). Leaf size: 34
dsolve((8*x^2*y(x)^3-2*y(x)^4)+(5*x^3*y(x)^2-8*x*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 0 \\ y \left (x \right ) &= \operatorname {RootOf}\left (x^{6} \textit {\_Z}^{48}-x^{6} \textit {\_Z}^{30}-c_{1} \right )^{18} x^{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.924 (sec). Leaf size: 411
DSolve[(8*x^2*y[x]^3-2*y[x]^4)+(5*x^3*y[x]^2-8*x*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 \\ y(x)\to \text {Root}\left [-\text {$\#$1}^8+3 \text {$\#$1}^7 x^2-3 \text {$\#$1}^6 x^4+\text {$\#$1}^5 x^6+\frac {e^{18 c_1}}{x^2}\&,1\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^8+3 \text {$\#$1}^7 x^2-3 \text {$\#$1}^6 x^4+\text {$\#$1}^5 x^6+\frac {e^{18 c_1}}{x^2}\&,2\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^8+3 \text {$\#$1}^7 x^2-3 \text {$\#$1}^6 x^4+\text {$\#$1}^5 x^6+\frac {e^{18 c_1}}{x^2}\&,3\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^8+3 \text {$\#$1}^7 x^2-3 \text {$\#$1}^6 x^4+\text {$\#$1}^5 x^6+\frac {e^{18 c_1}}{x^2}\&,4\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^8+3 \text {$\#$1}^7 x^2-3 \text {$\#$1}^6 x^4+\text {$\#$1}^5 x^6+\frac {e^{18 c_1}}{x^2}\&,5\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^8+3 \text {$\#$1}^7 x^2-3 \text {$\#$1}^6 x^4+\text {$\#$1}^5 x^6+\frac {e^{18 c_1}}{x^2}\&,6\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^8+3 \text {$\#$1}^7 x^2-3 \text {$\#$1}^6 x^4+\text {$\#$1}^5 x^6+\frac {e^{18 c_1}}{x^2}\&,7\right ] \\ y(x)\to \text {Root}\left [-\text {$\#$1}^8+3 \text {$\#$1}^7 x^2-3 \text {$\#$1}^6 x^4+\text {$\#$1}^5 x^6+\frac {e^{18 c_1}}{x^2}\&,8\right ] \\ y(x)\to 0 \\ \end{align*}