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]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y=-{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
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)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (c_{3} {\mathrm e}^{2 x}+4 x^{3}+c_{2} {\mathrm e}^{x}-x^{2}+c_{1} -17 x \right ) \]
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 47
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]
\[ y(x)\to \frac {1}{2} e^x \left (8 x^3-2 x^2-34 x+2 c_2 e^x+2 c_3 e^{2 x}-49+2 c_1\right ) \]