64.7.5 problem 5

Internal problem ID [13379]
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
Date solved : Tuesday, January 28, 2025 at 05:36:10 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.160 (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)
 

\[ y = \frac {\operatorname {RootOf}\left (-\ln \left (x \right )+c_{1} +\ln \left (\textit {\_Z} +2\right )+4 \ln \left (\textit {\_Z} \right )\right )}{x} \]

✓ Solution by Mathematica

Time used: 0.203 (sec). Leaf size: 64

DSolve[(4*x*y[x]^2+6*y[x])+(5*x^2*y[x]+8*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [6^{2/3} \log (x)+20 c_1=20 \int _1^{\frac {5 x y(x)+16}{\sqrt [3]{6} (5 x y(x)+8)}}\frac {1}{K[1]^3-\frac {7 K[1]}{6^{2/3}}+1}dK[1],y(x)\right ] \]