Internal problem ID [10236]
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]]
\[ \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-{\mathrm e}^{{\mathrm e}^{x}}=0} \]
✓ 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)
\[ y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{x}-2 x}-{\mathrm e}^{-2 x} c_{1} +c_{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.016 (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*}