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]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y=-{\mathrm e}^{x} \left (7+6 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
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)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{2} -\frac {{\mathrm e}^{x} \left (x^{3}-2 c_{3} x +2 x^{2}-2 c_{1} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 41
DSolve[y'''[x]-y''[x]-y'[x]+y[x]==-Exp[x]*(7+6*x),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x \left (-\frac {x^3}{2}-x^2+x+c_3 x-\frac {1}{2}+c_2\right )+c_1 e^{-x} \]