Internal problem ID [1502]
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 5.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }-3 y-{\mathrm e}^{x} \left (16 x^{3}+24 x^{2}+2 x -1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 76
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)-diff(y(x),x)-3*y(x)=exp(x)*(-1+2*x+24*x^2+16*x^3),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (x^{3}-x^{2}+x -1\right ) \left (16 \,{\mathrm e}^{x} x^{3}+24 x^{2} {\mathrm e}^{x}+2 x \,{\mathrm e}^{x}-{\mathrm e}^{x}\right )}{32 x^{3}+48 x^{2}+4 x -2}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{-3 x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 46
DSolve[y'''[x]+3*y''[x]-y'[x]-3*y[x]==Exp[x]*(-1+2*x+24*x^2+16*x^3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^x \left (2 (x-1) x \left (x^2+1\right )+1+4 c_3\right )+c_1 e^{-3 x}+c_2 e^{-x} \\ \end{align*}