Internal problem ID [219]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+16 y-{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+16*y(x)=exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (4 x \right ) c_{2}+\cos \left (4 x \right ) c_{1}+\frac {{\mathrm e}^{3 x}}{25} \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 29
DSolve[y''[x]+16*y[x]==Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {e^{3 x}}{25}+c_1 \cos (4 x)+c_2 \sin (4 x) \\ \end{align*}