Internal problem ID [1550]
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 53.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y=4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 \cos \left (x \right ) x +2 \sin \left (x \right ) \left (1+x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve(1*diff(y(x),x$3)+1*diff(y(x),x$2)-1*diff(y(x),x)-1*y(x)=4*exp(-x)*(1-6*x)-2*x*cos(x)+2*(1+x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} \left ({\mathrm e}^{x} \cos \left (x \right ) x +2 x^{3}-2 \sin \left (x \right ) {\mathrm e}^{x}+2 x^{2}+2 x +1\right )+c_{1} {\mathrm e}^{x}+{\mathrm e}^{-x} c_{2} +c_{3} {\mathrm e}^{-x} x \]
✓ Solution by Mathematica
Time used: 0.627 (sec). Leaf size: 54
DSolve[1*y'''[x]+1*y''[x]-1*y'[x]-1*y[x]==4*Exp[-x]*(1-6*x)-2*x*Cos[x]+2*(1+x)*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (2 x^3+2 x^2+2 x-2 e^x \sin (x)+e^x x \cos (x)+c_2 x+c_3 e^{2 x}+1+c_1\right ) \]