Internal problem ID [1505]
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 8.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y+{\mathrm e}^{x} \left (7+6 x \right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(diff(y(x),x$3)-diff(y(x),x$2)-diff(y(x),x)+y(x)=-exp(x)*(7+6*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2+x \right ) x^{2} \left (-6 x \,{\mathrm e}^{x}-7 \,{\mathrm e}^{x}\right )}{12 x +14}+c_{1} {\mathrm e}^{x}+{\mathrm e}^{-x} c_{2} +c_{3} {\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 40
DSolve[y'''[x]-y''[x]-y'[x]+y[x]==-Exp[x]*(7+6*x),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (-\frac {1}{2} (x+2) x^2+(1+c_3) x-\frac {1}{2}+c_2\right )+c_1 e^{-x} \\ \end{align*}