62.24.2 problem Ex 2

Internal problem ID [12859]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 47. Particular integral. Page 100
Problem number : Ex 2
Date solved : Monday, March 31, 2025 at 07:22:55 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{{\mathrm e}^{x}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)+2*y(x) = exp(exp(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_2 \,{\mathrm e}^{x}+{\mathrm e}^{{\mathrm e}^{x}}-c_1 \right ) {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.046 (sec). Leaf size: 47

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

\[ y(x)\to e^{-2 x} \left (\int _1^x-e^{2 K[1]+e^{K[1]}}dK[1]+e^{x+e^x}+c_2 e^x+c_1\right ) \]

✓ Sympy. Time used: 0.484 (sec). Leaf size: 17

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

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