Internal problem ID [6047]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 99. Clairaut’s equation. EXERCISES Page
320
Problem number: 8.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {x^{8} \left (y^{\prime }\right )^{2}+3 x y^{\prime }+9 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.282 (sec). Leaf size: 42
dsolve(x^8*diff(y(x),x)^2+3*x*diff(y(x),x)+9*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{4 x^{6}} \\ y \relax (x ) = \frac {-x^{3}+c_{1}}{x^{3} c_{1}^{2}} \\ y \relax (x ) = -\frac {x^{3}+c_{1}}{x^{3} c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.009 (sec). Leaf size: 130
DSolve[x^8*(y'[x])^2+3*x*y'[x]+9*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {x \sqrt {4 x^6 y(x)-1} \text {ArcTan}\left (\sqrt {4 x^6 y(x)-1}\right )}{3 \sqrt {x^2-4 x^8 y(x)}}-\frac {1}{6} \log (y(x))=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {\sqrt {x^2-4 x^8 y(x)} \text {ArcTan}\left (\sqrt {4 x^6 y(x)-1}\right )}{3 x \sqrt {4 x^6 y(x)-1}}-\frac {1}{6} \log (y(x))=c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}