Internal problem ID [1547]
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 50.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-y^{\prime }+2 x +2-4 \,{\mathrm e}^{x}+6 \,{\mathrm e}^{-x}-96 \,{\mathrm e}^{3 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 51
dsolve(1*diff(y(x),x$3)-0*diff(y(x),x$2)-1*diff(y(x),x)-0*y(x)=-2*(1+x)+4*exp(x)-6*exp(-x)+96*exp(3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}-{\mathrm e}^{-x} c_{1}+x^{2}+2 x \,{\mathrm e}^{x}-3 \,{\mathrm e}^{x}-3 x \,{\mathrm e}^{-x}-\frac {9 \,{\mathrm e}^{-x}}{2}+4 \,{\mathrm e}^{3 x}+2 x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.2 (sec). Leaf size: 49
DSolve[1*y'''[x]-0*y''[x]-1*y'[x]-0*y[x]==-2*(1+x)+4*Exp[x]-6*Exp[-x]+96*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (x+2)+4 e^{3 x}+e^x (2 x-3+c_1)-\frac {1}{2} e^{-x} (6 x+9+2 c_2)+c_3 \\ \end{align*}