Internal problem ID [236]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 33.
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-\sin \left (2 x \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)+9*y(x)=sin(2*x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\frac {8 \left (\cos ^{2}\relax (x )\right ) \sin \relax (x )}{15}+\frac {2 \cos \relax (x ) \sin \relax (x )}{5}+\frac {2 \sin \relax (x )}{15}+4 \left (\cos ^{3}\relax (x )\right )-3 \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 26
DSolve[{y''[x]+9*y[x]==Sin[2*x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} \sin (2 x)-\frac {2}{15} \sin (3 x)+\cos (3 x) \\ \end{align*}