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]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime }=-2-2 x +4 \,{\mathrm e}^{x}-6 \,{\mathrm e}^{-x}+96 \,{\mathrm e}^{3 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
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)
\[ y \left (x \right ) = \frac {\left (-6 x -2 c_{2} -9\right ) {\mathrm e}^{-x}}{2}+4 \,{\mathrm e}^{3 x}+\left (2 x -3+c_{1} \right ) {\mathrm e}^{x}+x^{2}+2 x +c_{3} \]
✓ Solution by Mathematica
Time used: 1.399 (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]
\[ y(x)\to x (x+2)+4 e^{3 x}+e^x (2 x-3+c_1)-\frac {1}{2} e^{-x} (6 x+9+2 c_2)+c_3 \]