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]]
\[ \boxed {y^{\prime \prime }+9 y=\sin \left (2 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = -\frac {2 \sin \left (3 x \right )}{15}+\cos \left (3 x \right )+\frac {\sin \left (2 x \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 26
DSolve[{y''[x]+9*y[x]==Sin[2*x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} \sin (2 x)-\frac {2}{15} \sin (3 x)+\cos (3 x) \]