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]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y={\mathrm e}^{2 x}-4 \,{\mathrm e}^{x}-2 \cos \left (x \right )+4 \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\left (\cos \left (x \right ) {\mathrm e}^{x}-2 \,{\mathrm e}^{2 x} x^{2}+2 \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{2 x} x -x \,{\mathrm e}^{3 x}-4 \,{\mathrm e}^{2 x}\right ) {\mathrm e}^{-x}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.373 (sec). Leaf size: 38
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]
\[ y(x)\to -\cos (x)+e^x \left (2 x^2+(4+c_2) x+e^x (x-2+c_3)+4+c_1\right ) \]