71.11.5 problem 5

Internal problem ID [14514]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 06:42:52 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y&=36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 41

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+21*diff(y(x),x)-26*y(x)=36*exp(2*x)*sin(3*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{2 x} \left (3 c_{3} \sin \left (3 x \right )-6 x \sin \left (3 x \right )+3 c_{2} \cos \left (3 x \right )-2 \cos \left (3 x \right )+3 c_{1} \right )}{3} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 82

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+21*D[y[x],x]-26*y[x]==36*Exp[2*x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (\sin (3 x) \int _1^x-4 \sin ^2(3 K[1])dK[1]+\int _1^x4 \sin (3 K[3])dK[3]+\cos (3 x) \int _1^x-2 \sin (6 K[2])dK[2]+c_2 \cos (3 x)+c_1 \sin (3 x)+c_3\right ) \]