75.2.1 problem 21

Internal problem ID [16607]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 21
Date solved : Monday, March 31, 2025 at 03:01:21 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (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: 0.002 (sec). Leaf size: 16

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

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

✓ Sympy. Time used: 0.121 (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)
 

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