56.1.6 problem 6

Internal problem ID [8718]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 6
Date solved : Sunday, March 30, 2025 at 01:24:48 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 12

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

\[ y = \frac {1}{2} x^{2}+x +c_1 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.111 (sec). Leaf size: 10

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

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