Internal problem ID [2207]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }+4 y=\frac {{\mathrm e}^{3 x}}{2}-\frac {{\mathrm e}^{-3 x}}{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=1/2*(exp(3*x)-exp(-3*x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (-25+{\mathrm e}^{6 x}+50 \,{\mathrm e}^{x} \left (c_{1} x +c_{2} \right )\right ) {\mathrm e}^{-3 x}}{50} \]
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 33
DSolve[y''[x]+4*y'[x]+4*y[x]==1/2*(Exp[3*x]-Exp[-3*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{50} e^{-3 x} \left (e^{6 x}+50 e^x (c_2 x+c_1)-25\right ) \]