Internal problem ID [2215]
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: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+5 y=\frac {{\mathrm e}^{x}}{2}+\frac {{\mathrm e}^{-x}}{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+5*y(x)=1/2*(exp(x)+exp(-x)),y(x), singsol=all)
\[ y = {\mathrm e}^{-2 x} \sin \left (x \right ) c_{2} +{\mathrm e}^{-2 x} \cos \left (x \right ) c_{1} +\frac {{\mathrm e}^{x}}{20}+\frac {{\mathrm e}^{-x}}{4} \]
✓ Solution by Mathematica
Time used: 0.203 (sec). Leaf size: 37
DSolve[y''[x]+4*y'[x]+5*y[x]==1/2*(Exp[x]+Exp[-x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{20} e^{-2 x} \left (5 e^x+e^{3 x}+20 c_2 \cos (x)+20 c_1 \sin (x)\right ) \]