Internal problem ID [10908]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {k x}{y^{4}}=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 91
dsolve(diff(y(x),x$2)+k*x/(y(x)^4)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \operatorname {RootOf}\left (-15 \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {-3 c_{1} \textit {\_f}^{4}+150 \textit {\_f} k}\, \textit {\_f}}{c_{1} \textit {\_f}^{3}-50 k}d \textit {\_f} \right ) x +5 x c_{2} +3\right ) x \\ y \left (x \right ) = \operatorname {RootOf}\left (15 \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {-3 c_{1} \textit {\_f}^{4}+150 \textit {\_f} k}\, \textit {\_f}}{c_{1} \textit {\_f}^{3}-50 k}d \textit {\_f} \right ) x +5 x c_{2} +3\right ) x \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]+k*x/(y[x]^4)==0,y[x],x,IncludeSingularSolutions -> True]
Not solved