21.1.4 problem 4

Internal problem ID [4080]
Book : Differential equations, Shepley L. Ross, 1964
Section : 2.4, page 55
Problem number : 4
Date solved : Monday, January 27, 2025 at 08:07:43 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: 0.061 (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: 1.969 (sec). Leaf size: 156

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]
 

\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*}