Internal problem ID [1507]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined
Coefficients for Higher Order Equations. Page 495
Problem number: section 9.3, problem 10.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y-2 \,{\mathrm e}^{3 x} \left (11-24 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 55
dsolve(diff(y(x),x$3)-5*diff(y(x),x$2)+3*diff(y(x),x)+9*y(x)=2*exp(3*x)*(11-24*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (8 x -17\right ) \left (-48 x \,{\mathrm e}^{3 x}+22 \,{\mathrm e}^{3 x}\right )}{192 x -88}+{\mathrm e}^{-x} c_{1}+c_{2} {\mathrm e}^{3 x}+c_{3} {\mathrm e}^{3 x} x \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 45
DSolve[y'''[x]-5*y''[x]+3*y'[x]+9*y[x]==2*Exp[3*x]*(11-24*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{-x}+e^{3 x} \left (\frac {1}{8} x (2 (17-8 x) x-17+8 c_3)+\frac {17}{32}+c_2\right ) \\ \end{align*}