71.13.12 problem 12

Internal problem ID [14532]
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
Date solved : Tuesday, January 28, 2025 at 06:43:02 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }+6 y&=-2 \sin \left (3 x \right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 10.879 (sec). Leaf size: 46

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)
 

\[ y = -\frac {13 \,{\mathrm e}^{\frac {x}{2}} \sqrt {23}\, \sin \left (\frac {\sqrt {23}\, x}{2}\right )}{69}+\frac {{\mathrm e}^{\frac {x}{2}} \cos \left (\frac {\sqrt {23}\, x}{2}\right )}{3}-\frac {\cos \left (3 x \right )}{3}+\frac {\sin \left (3 x \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 67

DSolve[{D[y[x],{x,2}]-D[y[x],x]+6*y[x]==-2*Sin[3*x],{y[0]==0,Derivative[1][y][0] ==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{69} \left (23 \sin (3 x)-13 \sqrt {23} e^{x/2} \sin \left (\frac {\sqrt {23} x}{2}\right )-23 \cos (3 x)+23 e^{x/2} \cos \left (\frac {\sqrt {23} x}{2}\right )\right ) \]