Internal problem ID [11812]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=8 \sin \left (2 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 6, y^{\prime }\left (0\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(x),x$2)+4*y(x)=8*sin(2*x),y(0) = 6, D(y)(0) = 8],y(x), singsol=all)
\[ y \left (x \right ) = \left (-2 x +6\right ) \cos \left (2 x \right )+5 \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 19
DSolve[{y''[x]+4*y[x]==8*Sin[2*x],{y[0]==0,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 \sin (x) \cos (x)-2 x \cos (2 x) \]