Internal problem ID [1540]
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 43.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+32 y^{\prime \prime }+64 y^{\prime }+39 y-{\mathrm e}^{-2 x} \left (\left (4-15 x \right ) \cos \left (3 x \right )-\left (4+15 x \right ) \sin \left (3 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 77
dsolve(1*diff(y(x),x$4)+8*diff(y(x),x$3)+32*diff(y(x),x$2)+64*diff(y(x),x)+39*y(x)=exp(-2*x)*((4-15*x)*cos(3*x)-(4+15*x)*sin(3*x)),y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-2 x} \left (30 x^{2}-30 x -11\right ) \cos \left (3 x \right )}{240}+\frac {{\mathrm e}^{-2 x} \left (30 x^{2}+30 x -11\right ) \sin \left (3 x \right )}{240}+c_{1} {\mathrm e}^{-3 x}+{\mathrm e}^{-x} c_{2}+c_{3} {\mathrm e}^{-2 x} \cos \left (3 x \right )+c_{4} {\mathrm e}^{-2 x} \sin \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.302 (sec). Leaf size: 67
DSolve[1*y''''[x]+8*y'''[x]+32*y''[x]+64*y'[x]+39*y[x]==Exp[-2*x]*((4-15*x)*Cos[3*x]-(4+15*x)*Sin[3*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-3 x} \left (c_4 e^{2 x}+c_3\right )+\frac {1}{720} e^{-2 x} ((-90 (x-1) x+25+720 c_2) \cos (3 x)+(90 x (x+1)-41+720 c_1) \sin (3 x)) \\ \end{align*}