Internal problem ID [2181]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y={\mathrm e}^{x}+\sin \left (4 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+9*y(x)=exp(x)+sin(4*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} +\frac {{\mathrm e}^{x}}{10}-\frac {\sin \left (4 x \right )}{7} \]
✓ Solution by Mathematica
Time used: 0.194 (sec). Leaf size: 35
DSolve[y''[x]+9*y[x]==Exp[x]+Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{10}-\frac {1}{7} \sin (4 x)+c_1 \cos (3 x)+c_2 \sin (3 x) \]