Internal problem ID [12256]
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: 0.078 (sec). Leaf size: 97
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 \sqrt {3}\, \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {-\textit {\_f}^{4} c_{1} +50 \textit {\_f} k}\, \textit {\_f}}{\textit {\_f}^{3} c_{1} -50 k}d \textit {\_f} \right ) x -5 c_{2} x -3\right ) x \\ y \left (x \right ) &= \operatorname {RootOf}\left (15 \sqrt {3}\, \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {-\textit {\_f}^{4} c_{1} +50 \textit {\_f} k}\, \textit {\_f}}{\textit {\_f}^{3} c_{1} -50 k}d \textit {\_f} \right ) x +5 c_{2} x +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