60.1.423 problem 434

Internal problem ID [10437]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 434
Date solved : Sunday, March 30, 2025 at 04:43:17 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-1&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 7

ode:=diff(y(x),x)-1 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x +c_1 \]

✓ Mathematica. Time used: 0.078 (sec). Leaf size: 45

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

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

✓ Sympy. Time used: 0.035 (sec). Leaf size: 5

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

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