Internal problem ID [12796]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }+6 y=-2 \sin \left (3 x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 6.438 (sec). Leaf size: 45
dsolve([diff(y(x),x$2)-diff(y(x),x)+6*y(x)=-2*sin(3*x),y(0) = 0, D(y)(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {13 \,{\mathrm e}^{\frac {x}{2}} \sqrt {23}\, \sin \left (\frac {\sqrt {23}\, x}{2}\right )}{69}+\frac {{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {23}\, x}{2}\right )}{3}+\frac {\sin \left (3 x \right )}{3}-\frac {\cos \left (3 x \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 67
DSolve[{y''[x]-y'[x]+6*y[x]==-2*Sin[3*x],{y[0]==0,y'[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{69} \left (23 \sin (3 x)-13 \sqrt {23} e^{x/2} \sin \left (\frac {\sqrt {23} x}{2}\right )-23 \cos (3 x)+23 e^{x/2} \cos \left (\frac {\sqrt {23} x}{2}\right )\right ) \]