75.13.5 problem 322

Internal problem ID [16839]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 13. Basic concepts and definitions. Exercises page 98
Problem number : 322
Date solved : Monday, March 31, 2025 at 03:23:56 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{4}&=1 \end{align*}

✓ Maple. Time used: 0.042 (sec). Leaf size: 31

ode:=diff(y(x),x)^4 = 1; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -i x +c_1 \\ y &= i x +c_1 \\ y &= x +c_1 \\ y &= -x +c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 43

ode=D[y[x],x]*D[y[x],x]^3==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -x+c_1 \\ y(x)\to c_1-i x \\ y(x)\to i x+c_1 \\ y(x)\to x+c_1 \\ \end{align*}

✓ Sympy. Time used: 0.219 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x)**4 - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} - i x, \ y{\left (x \right )} = C_{1} + i x, \ y{\left (x \right )} = C_{1} - x, \ y{\left (x \right )} = C_{1} + x\right ] \]