Internal problem ID [13237]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.5 (b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y={\mathrm e}^{3 x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve([diff(y(x),x$3)-9*diff(y(x),x$2)+27*diff(y(x),x)-27*y(x)=exp(3*x)*sin(x),exp(3*x)],y(x), singsol=all)
\[ y = x^{2} {\mathrm e}^{3 x} c_{3} +x \,{\mathrm e}^{3 x} c_{2} +{\mathrm e}^{3 x} \cos \left (x \right )+{\mathrm e}^{3 x} c_{1} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 25
DSolve[y'''[x]-9*y''[x]+27*y'[x]-27*y[x]==Exp[3*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{3 x} (\cos (x)+x (c_3 x+c_2)+c_1) \]