Internal problem ID [1503]
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 6.
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}^{x} \left (15 x^{2}+34 x +14\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 61
dsolve(diff(y(x),x$3)+diff(y(x),x$2)-2*y(x)=exp(x)*(14+34*x+15*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2} \left (x +1\right ) \left (15 x^{2} {\mathrm e}^{x}+34 x \,{\mathrm e}^{x}+14 \,{\mathrm e}^{x}\right )}{15 x^{2}+34 x +14}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x} \cos \relax (x )+c_{3} \sin \relax (x ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.136 (sec). Leaf size: 44
DSolve[y'''[x]+y''[x]-2*y[x]==Exp[x]*(14+34*x+15*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} e^x \left (5 (x+1) x^2-2+5 c_3\right )+e^{-x} (c_2 \cos (x)+c_1 \sin (x)) \\ \end{align*}