75.2.2 problem 22

Internal problem ID [16600]
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 : 22
Date solved : Thursday, March 13, 2025 at 08:25:37 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = -x -1+{\mathrm e}^{x} c_{1} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 28

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

\[ y(x)\to e^x \left (\int _1^xe^{-K[1]} K[1]dK[1]+c_1\right ) \]

✓ Sympy. Time used: 0.103 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = C_{1} e^{x} - x - 1 \]