Internal problem ID [1557]
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 60.
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 }-y^{\prime }+y-{\mathrm e}^{2 x} \left (10+3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 45
dsolve(diff(y(x),x$3)-1*diff(y(x),x$2)-1*diff(y(x),x)+1*y(x)=exp(2*x)*(10+3*x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (x +1\right ) \left (3 \,{\mathrm e}^{2 x} x +10 \,{\mathrm e}^{2 x}\right )}{10+3 x}+{\mathrm e}^{x} c_{1}+{\mathrm e}^{-x} c_{2}+c_{3} {\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 34
DSolve[y'''[x]-1*y''[x]-1*y'[x]+1*y[x]==Exp[2*x]*(10+3*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} (x+1)+c_1 e^{-x}+e^x (c_3 x+c_2) \\ \end{align*}