Internal problem ID [1565]
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 68.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+14 y^{\prime \prime }-20 y^{\prime }+25 y-{\mathrm e}^{x} \left (\left (6 x +2\right ) \cos \left (2 x \right )+3 \sin \left (2 x \right )\right )=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 75
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+14*diff(y(x),x$2)-20*diff(y(x),x)+25*y(x)=exp(x)*((2+6*x)*cos(2*x)+3*sin(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (4 x^{3}+4 x^{2}+126 x -41\right ) \cos \left (2 x \right )}{64}+\frac {{\mathrm e}^{x} \left (6 x +1111\right ) \sin \left (2 x \right )}{192}+c_{1} {\mathrm e}^{x} \cos \left (2 x \right )+c_{2} {\mathrm e}^{x} \sin \left (2 x \right )+c_{3} {\mathrm e}^{x} \cos \left (2 x \right ) x +c_{4} {\mathrm e}^{x} \sin \left (2 x \right ) x \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 74
DSolve[y''''[x]-4*y'''[x]+14*y''[x]-20*y'[x]+25*y[x]==Exp(x)*((2+6*x)*Cos[2*x]+3*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\text {Exp} (17 x (816 x+3053)+68676) \sin (2 x)}{83521}-\frac {2 \text {Exp} (255 x (51 x+245)+100292) \cos (2 x)}{83521}+e^x (c_4 x+c_3) \cos (2 x)+e^x (c_2 x+c_1) \sin (2 x) \\ \end{align*}