58.1.5 problem 5

Internal problem ID [9076]
Book : Second order enumerated odes
Section : section 1
Problem number : 5
Date solved : Sunday, March 30, 2025 at 02:06:19 PM
CAS classification : [[_2nd_order, _quadrature]]

\begin{align*} a {y^{\prime \prime }}^{2}&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 9

ode:=a*diff(diff(y(x),x),x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 x +c_2 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 12

ode=a*(D[y[x],{x,2}])^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_2 x+c_1 \]

✓ Sympy. Time used: 0.039 (sec). Leaf size: 7

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

\[ y{\left (x \right )} = C_{1} + C_{2} x \]