67.2.35 problem Problem 15

Internal problem ID [13992]
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
Date solved : Tuesday, January 28, 2025 at 08:25:11 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\frac {k x}{y^{4}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.133 (sec). Leaf size: 97

dsolve(diff(y(x),x$2)+k*x/(y(x)^4)=0,y(x), singsol=all)
 

\begin{align*} y &= \operatorname {RootOf}\left (15 \sqrt {3}\, \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {-c_{1} \textit {\_f}^{4}+50 \textit {\_f} k}\, \textit {\_f}}{c_{1} \textit {\_f}^{3}-50 k}d \textit {\_f} \right ) x -5 c_{2} x -3\right ) x \\ y &= \operatorname {RootOf}\left (15 \sqrt {3}\, \left (\int _{}^{\textit {\_Z}}\frac {\sqrt {-c_{1} \textit {\_f}^{4}+50 \textit {\_f} k}\, \textit {\_f}}{c_{1} \textit {\_f}^{3}-50 k}d \textit {\_f} \right ) x +5 c_{2} x +3\right ) x \\ \end{align*}

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],{x,2}]+k*x/(y[x]^4)==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved