Internal problem ID [1548]
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 51.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+9 y^{\prime }-10 y-10 \,{\mathrm e}^{2 x}-20 \,{\mathrm e}^{x} \sin \left (2 x \right )+10=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 91
dsolve(1*diff(y(x),x$3)-4*diff(y(x),x$2)+9*diff(y(x),x)-10*y(x)=10*exp(2*x)+20*exp(x)*sin(2*x)-10,y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{-2 x} {\mathrm e}^{3 x} \left (5 x -8\right ) \cos \left (2 x \right )}{5}-\frac {{\mathrm e}^{-2 x} {\mathrm e}^{3 x} \left (20 x +13\right ) \sin \left (2 x \right )}{10}+\frac {{\mathrm e}^{-2 x} \left (10 \,{\mathrm e}^{4 x} x +5 \,{\mathrm e}^{2 x}-4 \,{\mathrm e}^{4 x}\right )}{5}+c_{1} {\mathrm e}^{2 x}+c_{2} {\mathrm e}^{x} \cos \left (2 x \right )+c_{3} {\mathrm e}^{x} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.578 (sec). Leaf size: 58
DSolve[1*y'''[x]-4*y''[x]+9*y'[x]-10*y[x]==10*Exp[2*x]+20*Exp[x]*Sin[2*x]-10,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{2 x} \left (2 x-\frac {4}{5}+c_3\right )+\frac {1}{20} e^x ((20 x-22+20 c_2) \cos (2 x)+(-40 x-21+20 c_1) \sin (2 x))+1 \\ \end{align*}