Internal problem ID [1559]
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 62.
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}^{2 x} \left (-3 x^{2}-4 x +5\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 67
dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=exp(2*x)*(5-4*x-3*x^2),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x \left (x^{2}+2 x +1\right ) \left (-3 \,{\mathrm e}^{2 x} x^{2}-4 \,{\mathrm e}^{2 x} x +5 \,{\mathrm e}^{2 x}\right )}{3 x^{2}+4 x -5}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 33
DSolve[y'''[x]-6*y''[x]+11*y'[x]-6*y[x]==Exp[2*x]*(5-4*x-3*x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x \left (e^x \left (x (x+1)^2+c_3 e^x+4+c_2\right )+c_1\right ) \\ \end{align*}