Internal problem ID [1537]
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 40.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+13 y^{\prime \prime }+12 y^{\prime }+4 y={\mathrm e}^{-x} \left (\left (4-x \right ) \cos \left (x \right )-\left (x +5\right ) \sin \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 65
dsolve(1*diff(y(x),x$4)+6*diff(y(x),x$3)+13*diff(y(x),x$2)+12*diff(y(x),x)+4*y(x)=exp(-1*x)*((4-x)*cos(x)-(5+x)*sin(x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-x} \cos \left (x \right )}{2}+\frac {\sin \left (x \right ) {\mathrm e}^{-x} x}{2}-\sin \left (x \right ) {\mathrm e}^{-x}-\frac {\cos \left (x \right ) {\mathrm e}^{-x} x}{2}+{\mathrm e}^{-2 x} c_{1} +{\mathrm e}^{-x} c_{2} +c_{3} {\mathrm e}^{-x} x +c_{4} {\mathrm e}^{-2 x} x \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 56
DSolve[1*y''''[x]+6*y'''[x]+13*y''[x]+12*y'[x]+4*y[x]==Exp[-1*x]*((4-x)*Cos[x]-(5+x)*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-2 x} \left (e^x (x-2) \sin (x)-e^x (x+1) \cos (x)+2 \left (c_2 x+c_3 e^x+c_4 e^x x+c_1\right )\right ) \]