52.1.10 problem 10

Internal problem ID [10381]
Book : Second order enumerated odes
Section : section 1
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 07:22:48 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} {y^{\prime \prime }}^{2}&=x \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)^2 = x; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {4 x^{{5}/{2}}}{15}+c_1 x +c_2 \\ y &= -\frac {4 x^{{5}/{2}}}{15}+c_1 x +c_2 \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 41

ode=(D[y[x],{x,2}])^2==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {4 x^{5/2}}{15}+c_2 x+c_1\\ y(x)&\to \frac {4 x^{5/2}}{15}+c_2 x+c_1 \end{align*}

✓ Sympy. Time used: 0.231 (sec). Leaf size: 31

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

\[ \left [ y{\left (x \right )} = C_{1} + C_{2} x - \frac {4 x^{\frac {5}{2}}}{15}, \ y{\left (x \right )} = C_{1} + C_{2} x + \frac {4 x^{\frac {5}{2}}}{15}\right ] \]