14.3 problem 3

Internal problem ID [2204]

Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section: Exercise 23, page 106
Problem number: 3.
ODE order: 2.
ODE degree: 1.

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

\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=1/2*(exp(x)+exp(-x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{3 x}+18 c_{1} x +9 \,{\mathrm e}^{x}+18 c_{2} \right ) {\mathrm e}^{-2 x}}{18} \]

Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 34

DSolve[y''[x]+4*y'[x]+4*y[x]==1/2*(Exp[x]+Exp[-x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{18} e^{-2 x} \left (9 e^x+e^{3 x}+18 (c_2 x+c_1)\right ) \]