Internal problem ID [1529]
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 32.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y+{\mathrm e}^{x} \left (\left (4 x^{2}+5 x +9\right ) \cos \left (2 x \right )-\left (-3 x^{2}-5 x +6\right ) \sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(1*diff(y(x),x$3)-2*diff(y(x),x$2)+1*diff(y(x),x)-2*y(x)=-exp(x)*((9+5*x+4*x^2)*cos(2*x)-(6-5*x-3*x^2)*sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (55 x +61\right ) {\mathrm e}^{x} \cos \left (2 x \right )}{50}+\frac {\left (25 x^{2}+15 x -27\right ) {\mathrm e}^{x} \sin \left (2 x \right )}{50}+c_{1} \cos \relax (x )+c_{2} \sin \relax (x )+c_{3} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 65
DSolve[1*y'''[x]-2*y''[x]+1*y'[x]-2*y[x]==Exp[2*x]*((9+5*x+4*x^2)*Cos[2*x]-(6-5*x-3*x^2)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_3 e^{2 x}+\frac {e^{2 x} ((520 (34-13 x) x+29907) \sin (2 x)-2 (65 x (91 x+113)+3928) \cos (2 x))}{43940}+c_1 \cos (x)+c_2 \sin (x) \\ \end{align*}