56.1.7 problem 7

Internal problem ID [8719]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 7
Date solved : Sunday, March 30, 2025 at 01:24:49 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = \frac {x^{2}}{2}+c_1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 15

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

\[ y(x)\to \frac {x^2}{2}+c_1 \]

✓ Sympy. Time used: 0.044 (sec). Leaf size: 8

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

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