24.2 problem Ex 2

Internal problem ID [10240]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-{\mathrm e}^{{\mathrm e}^{x}}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 25

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

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

Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

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

\begin{align*} y(x)\to e^{-2 x} \left (e^{e^x}+c_2 e^x+c_1\right ) \\ \end{align*}