Internal problem ID [1558]
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 61.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-2 y+{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.011 (sec). Leaf size: 70
dsolve(diff(y(x),x$3)+1*diff(y(x),x$2)-0*diff(y(x),x)-2*y(x)=-exp(3*x)*(9+67*x+17*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x^{2}+2 x -2\right ) \left (-17 x^{2} {\mathrm e}^{3 x}-67 x \,{\mathrm e}^{3 x}-9 \,{\mathrm e}^{3 x}\right )}{34 x^{2}+134 x +18}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x} \cos \relax (x )+c_{3} \sin \relax (x ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.153 (sec). Leaf size: 45
DSolve[y'''[x]+1*y''[x]-0*y'[x]-2*y[x]==-Exp[3*x]*(9+67*x+17*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} e^{3 x} (x (x+2)-2)+c_3 e^x+e^{-x} (c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}