Internal problem ID [13362]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 21. Nonhomogeneous equations in general. Additional exercises page
391
Problem number: 21.10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+9 y=169 \sin \left (2 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -10, y^{\prime }\left (0\right ) = 9] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve([diff(y(x),x$2)+6*diff(y(x),x)+9*y(x)=169*sin(2*x),y(0) = -10, D(y)(0) = 9],y(x), singsol=all)
\[ y = \left (5 x +2\right ) {\mathrm e}^{-3 x}-12 \cos \left (2 x \right )+5 \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 34
DSolve[{y''[x]+6*y'[x]+9*y[x]==169*Sin[2*x],{y[0]==-10,y'[0]==9}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (5 x+5 e^{3 x} \sin (2 x)+2\right )-12 \cos (2 x) \]