Internal problem ID [6697]
Book: Second order enumerated odes
Section: section 2
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {10 y^{\prime \prime }+y^{\prime } x^{2}+\frac {3 \left (y^{\prime }\right )^{2}}{y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 70
dsolve(10*diff(y(x),x$2)+x^2*diff(y(x),x)+3/y(x)*(diff(y(x),x))^2=0,y(x), singsol=all)
\[ \frac {10 y \relax (x )^{\frac {13}{10}}}{13}-\frac {x \WhittakerM \left (\frac {1}{6}, \frac {2}{3}, \frac {x^{3}}{30}\right ) c_{1} {\mathrm e}^{-\frac {x^{3}}{60}} 3^{\frac {1}{3}} 300000^{\frac {5}{6}}}{40000 \left (x^{3}\right )^{\frac {1}{6}}}-\frac {30 c_{1} {\mathrm e}^{-\frac {x^{3}}{60}} \WhittakerM \left (\frac {7}{6}, \frac {2}{3}, \frac {x^{3}}{30}\right ) 30^{\frac {1}{6}}}{x^{2} \left (x^{3}\right )^{\frac {1}{6}}}-c_{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.597 (sec). Leaf size: 52
DSolve[10*y''[x]+x^2*y'[x]+3/y[x]*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \exp \left (\int _1^x\frac {30 e^{-\frac {1}{30} K[1]^3}}{30 c_1-13 E_{\frac {2}{3}}\left (\frac {K[1]^3}{30}\right ) K[1]}dK[1]\right ) \\ \end{align*}