69.1.13 problem 15

Internal problem ID [17963]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 15
Date solved : Thursday, October 02, 2025 at 02:31:33 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 2 y+y^{\prime }&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=diff(y(x),x)+2*y(x) = exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{x}}{3}+{\mathrm e}^{-2 x} c_1 \]

✓ Mathematica. Time used: 0.025 (sec). Leaf size: 21

ode=D[y[x],x]+2*y[x]==Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^x}{3}+c_1 e^{-2 x} \end{align*}

✓ Sympy. Time used: 0.075 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*y(x) - exp(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + \frac {e^{x}}{3} \]