Internal problem ID [13138]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 36.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational]
\[ \boxed {y^{2} x +\left (y x^{2}+10 y^{4}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x*y(x)^2+(x^2*y(x)+10*y(x)^4)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 \frac {x^{2} y \left (x \right )^{2}}{2}+2 y \left (x \right )^{5}+c_{1} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 3.953 (sec). Leaf size: 141
DSolve[x*y[x]^2+(x^2*y[x]+10*y[x]^4)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 0 y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,1\right ] y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,2\right ] y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,3\right ] y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,4\right ] y(x)\to \text {Root}\left [4 \text {$\#$1}^5+\text {$\#$1}^2 x^2-2 c_1\&,5\right ] y(x)\to 0 \end{align*}