85.29.1 problem 1

Internal problem ID [22615]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. C Exercises at page 60
Problem number : 1
Date solved : Thursday, October 02, 2025 at 08:55:05 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{\prime \prime }&=-\frac {4}{y^{3}} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=4 \\ y^{\prime }\left (2\right )&=0 \\ \end{align*}

✗ Maple

ode:=diff(diff(y(x),x),x) = -4/y(x)^3; 
ic:=[y(2) = 4, D(y)(2) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 23

ode=D[y[x],{x,2}]==-4/y[x]^3; 
ic={y[2]==4,Derivative[1][y][2] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \sqrt {-x^2+4 x+60} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) + 4/y(x)**3,0) 
ics = {y(2): 4, Subs(Derivative(y(x), x), x, 2): 0} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out