Internal problem ID [11807]
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: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+13 y=8 \sin \left (3 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 31
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+13*y(x)=8*sin(3*x),y(0) = 1, D(y)(0) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 \,{\mathrm e}^{2 x}+3\right ) \cos \left (3 x \right )}{5}+\frac {\sin \left (3 x \right ) \left ({\mathrm e}^{2 x}+1\right )}{5} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 36
DSolve[{y''[x]-4*y'[x]+13*y[x]==8*Sin[3*x],{y[0]==1,y'[0]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} \left (\left (e^{2 x}+1\right ) \sin (3 x)+\left (2 e^{2 x}+3\right ) \cos (3 x)\right ) \]