64.7.6 problem 6

Internal problem ID [13380]
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
Date solved : Tuesday, January 28, 2025 at 05:36:13 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 1.835 (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 &= 0 \\ y &= \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: 0.781 (sec). Leaf size: 105

DSolve[(8*x^2*y[x]^3-2*y[x]^4)+(5*x^3*y[x]^2-8*x*y[x]^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 0 \\ \text {Solve}\left [\frac {286^{2/3} x^2 \log (x)}{\sqrt [3]{-x^6}}+60 c_1&=60 \int _1^{\frac {16 x^2 y(x)-55 x^4}{\sqrt [3]{286} \sqrt [3]{-x^6} \left (5 x^2-8 y(x)\right )}}\frac {1}{K[1]^3+\frac {147 \sqrt [3]{-1} K[1]}{286^{2/3}}+1}dK[1],y(x)\right ] \\ \end{align*}