Internal problem ID [1498]
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 1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y+{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 63
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=-exp(x)*(4+76*x-24*x^2),y(x), singsol=all)
\[ y \relax (x ) = \frac {x \left (4 x^{2}-x -17\right ) \left (24 x^{2} {\mathrm e}^{x}-76 x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{x}\right )}{24 x^{2}-76 x -4}+{\mathrm e}^{x} c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 44
DSolve[y'''[x]-6*y''[x]+11*y'[x]-6*y[x]==-Exp[x]*(4+76*x-24*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} e^x \left (2 x (x (4 x-1)-17)+2 e^x \left (c_3 e^x+c_2\right )-49+2 c_1\right ) \\ \end{align*}