75.16.3 problem 476

Internal problem ID [16905]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 476
Date solved : Monday, March 31, 2025 at 03:35:07 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x) = exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-3 x} c_1}{3}+\frac {{\mathrm e}^{x}}{4}+c_2 \]

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 26

ode=D[y[x],{x,2}]+3*D[y[x],x]==Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^x}{4}-\frac {1}{3} c_1 e^{-3 x}+c_2 \]

✓ Sympy. Time used: 0.172 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(x) + 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{- 3 x} + \frac {e^{x}}{4} \]