55.1.1 problem 1.1.1

Internal problem ID [13221]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 1, First-Order differential equations
Problem number : 1.1.1
Date solved : Wednesday, October 01, 2025 at 03:37:14 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=f \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

\[ y = \int f \left (x \right )d x +c_1 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 18

ode=D[y[x],x]==f[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^xf(K[1])dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} + \int f{\left (x \right )}\, dx \]