Internal problem ID [1532]
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 35.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-7 y^{\prime \prime }+20 y^{\prime }-24 y+{\mathrm e}^{2 x} \left (\left (13-8 x \right ) \cos \left (2 x \right )-\left (8-4 x \right ) \sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 66
dsolve(1*diff(y(x),x$3)-7*diff(y(x),x$2)+20*diff(y(x),x)-24*y(x)=-exp(2*x)*((13-8*x)*cos(2*x)-(8-4*x)*sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (20 x^{2}-60 x +83\right ) {\mathrm e}^{2 x} \cos \left (2 x \right )}{40}+\frac {\left (10 x -47\right ) {\mathrm e}^{2 x} \sin \left (2 x \right )}{20}+{\mathrm e}^{3 x} c_{1}+c_{2} \cos \left (2 x \right ) {\mathrm e}^{2 x}+c_{3} \sin \left (2 x \right ) {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.357 (sec). Leaf size: 53
DSolve[1*y'''[x]-7*y''[x]+20*y'[x]-24*y[x]==-Exp[2*x]*((13-8*x)*Cos[2*x]-(8-4*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{40} e^{2 x} \left (40 c_3 e^x+(-20 (x-3) x+21+40 c_2) \cos (2 x)+(20 x-37+40 c_1) \sin (2 x)\right ) \\ \end{align*}