75.11.2 problem 261

Internal problem ID [16782]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 11. Singular solutions of differential equations. Exercises page 92
Problem number : 261
Date solved : Monday, March 31, 2025 at 03:17:20 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-4 y&=0 \end{align*}

✓ Maple. Time used: 0.080 (sec). Leaf size: 15

ode:=diff(y(x),x)^2-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= \left (x -c_1 \right )^{2} \\ \end{align*}

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 38

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

\begin{align*} y(x)\to \frac {1}{4} (-2 x+c_1){}^2 \\ y(x)\to \frac {1}{4} (2 x+c_1){}^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.306 (sec). Leaf size: 14

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

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