73.9.32 problem 14.5 (b)

Internal problem ID [15293]
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)
Date solved : Tuesday, January 28, 2025 at 07:51:40 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&={\mathrm e}^{3 x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

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),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 76

DSolve[D[y[x],{x,3}]-9*D[y[x],{x,2}]+27*D[y[x],x]-27*y[x]==Exp[3*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

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