Internal problem ID [4314]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-30 \sin \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+9*y(x)=30*sin(3*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (3 x \right ) c_{2}+\cos \left (3 x \right ) c_{1}-5 \cos \left (3 x \right ) x \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 31
DSolve[y''[x]+9*y[x]==30*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (-5 x+c_1) \cos (3 x)+\frac {1}{6} (5+6 c_2) \sin (3 x) \\ \end{align*}