Internal problem ID [1545]
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 48.
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 }+5 y^{\prime }-2 y-{\mathrm e}^{2 x}+4 \,{\mathrm e}^{x}+2 \cos \relax (x )-4 \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 67
dsolve(1*diff(y(x),x$3)-4*diff(y(x),x$2)+5*diff(y(x),x)-2*y(x)=exp(2*x)-4*exp(x)-2*cos(x)+4*sin(x),y(x), singsol=all)
\[ y \relax (x ) = -\left (\cos \relax (x ) {\mathrm e}^{x}-2 \,{\mathrm e}^{2 x} x^{2}-x \,{\mathrm e}^{3 x}+2 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{2 x} x -4 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.208 (sec). Leaf size: 36
DSolve[1*y'''[x]-4*y''[x]+5*y'[x]-2*y[x]==Exp[2*x]-4*Exp[x]-2*Cos[x]+4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\cos (x)+e^x \left (x (2 x+4+c_2)+e^x (x-2+c_3)+4+c_1\right ) \\ \end{align*}