62.24.2 problem Ex 2

Internal problem ID [12930]
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 : Tuesday, January 28, 2025 at 04:44:15 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(exp(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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