Internal problem ID [4173]
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]
\[ \boxed {x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = -\frac {1}{4 x^{4}} y \left (x \right ) = \frac {-2 x^{4}-c_{1}^{2}-c_{1} \left (2 i x^{2}-c_{1} \right )}{2 c_{1}^{2} x^{4}} y \left (x \right ) = \frac {-2 x^{4}-c_{1}^{2}-c_{1} \left (-2 i x^{2}-c_{1} \right )}{2 c_{1}^{2} x^{4}} y \left (x \right ) = \frac {-2 x^{4}+c_{1} \left (2 i x^{2}+c_{1} \right )-c_{1}^{2}}{2 c_{1}^{2} x^{4}} y \left (x \right ) = \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: 0.549 (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} \text {arctanh}\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} \text {arctanh}\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*}