Internal problem ID [2149]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-9 y={\mathrm e}^{3 x}+\sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-9*y(x)=exp(3*x)+sin(3*x),y(x), singsol=all)
\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{-3 x} c_{1} +\frac {\left (6 x -1\right ) {\mathrm e}^{3 x}}{36}-\frac {\sin \left (3 x \right )}{18} \]
✓ Solution by Mathematica
Time used: 0.247 (sec). Leaf size: 39
DSolve[y''[x]-9*y[x]==Exp[3*x]+Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{18} \sin (3 x)+e^{3 x} \left (\frac {x}{6}-\frac {1}{36}+c_1\right )+c_2 e^{-3 x} \]