Internal problem ID [4174]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 940.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = \frac {1}{4 x^{6}} y \left (x \right ) = \frac {-x^{3}+c_{1}}{x^{3} c_{1}^{2}} y \left (x \right ) = -\frac {x^{3}+c_{1}}{x^{3} c_{1}^{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.562 (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} \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)} \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*}