Internal problem ID [12778]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y=36 \,{\mathrm e}^{2 x} \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {{\mathrm e}^{2 x} \left (3 c_{3} \sin \left (3 x \right )-6 x \sin \left (3 x \right )+3 c_{2} \cos \left (3 x \right )-2 \cos \left (3 x \right )+3 c_{1} \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 34
DSolve[y'''[x]-6*y''[x]+21*y'[x]-26*y[x]==36*Exp[2*x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} ((-1+c_2) \cos (3 x)+(-2 x+c_1) \sin (3 x)+c_3) \]