Internal problem ID [3665]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 32
Problem number: 939.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x^{6} \left (y^{\prime }\right )^{2}-2 y^{\prime } x -4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 143
dsolve(x^6*diff(y(x),x)^2-2*x*diff(y(x),x)-4*y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {1}{4 x^{4}} \\ y \relax (x ) = \frac {-2 x^{4}-c_{1}^{2}-c_{1} \left (2 i x^{2}-c_{1}\right )}{2 c_{1}^{2} x^{4}} \\ y \relax (x ) = \frac {-2 x^{4}-c_{1}^{2}-c_{1} \left (-2 i x^{2}-c_{1}\right )}{2 c_{1}^{2} x^{4}} \\ y \relax (x ) = \frac {-2 x^{4}+c_{1} \left (2 i x^{2}+c_{1}\right )-c_{1}^{2}}{2 c_{1}^{2} x^{4}} \\ y \relax (x ) = \frac {-2 x^{4}+c_{1} \left (-2 i x^{2}+c_{1}\right )-c_{1}^{2}}{2 c_{1}^{2} x^{4}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.625 (sec). Leaf size: 128
DSolve[x^6 (y'[x])^2-2 x y'[x]-4 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [-\frac {x \sqrt {4 x^4 y(x)+1} \tanh ^{-1}\left (\sqrt {4 x^4 y(x)+1}\right )}{2 \sqrt {4 x^6 y(x)+x^2}}-\frac {1}{4} \log (y(x))=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {x \sqrt {4 x^4 y(x)+1} \tanh ^{-1}\left (\sqrt {4 x^4 y(x)+1}\right )}{2 \sqrt {4 x^6 y(x)+x^2}}-\frac {1}{4} \log (y(x))=c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}