Internal problem ID [1564]
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 67.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime \prime }-2 y^{\prime }-{\mathrm e}^{x} \left (\left (28+6 x \right ) \cos \left (2 x \right )+\left (11-12 x \right ) \sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 51
dsolve(diff(y(x),x$4)-3*diff(y(x),x$3)+4*diff(y(x),x$2)-2*diff(y(x),x)-0*y(x)=exp(x)*((28+6*x)*cos(2*x)+(11-12*x)*sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = -\sin \left (2 x \right ) {\mathrm e}^{x} x +\frac {3 \,{\mathrm e}^{x}}{2}+\frac {c_{2} \cos \relax (x ) {\mathrm e}^{x}}{2}+\frac {\sin \relax (x ) {\mathrm e}^{x} c_{2}}{2}-\frac {c_{3} \cos \relax (x ) {\mathrm e}^{x}}{2}+\frac {c_{3} \sin \relax (x ) {\mathrm e}^{x}}{2}+c_{1} {\mathrm e}^{x}+c_{4} \]
✓ Solution by Mathematica
Time used: 0.562 (sec). Leaf size: 78
DSolve[y''''[x]-3*y'''[x]+4*y''[x]-2*y'[x]-0*y[x]==Exp(x)*((28+6*x)*Cos[2*x]+(11-12*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\text {Exp} (20 x (15 x-8)-819) \sin (2 x)+2 \text {Exp} (5 x (60 x+143)+676) \cos (2 x)}{1000}+c_3 e^x+\frac {1}{2} e^x ((c_2-c_1) \cos (x)+(c_1+c_2) \sin (x))+c_4 \\ \end{align*}