Internal problem ID [1543]
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 46.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+32 y^{\prime \prime }-64 y^{\prime }+64 y={\mathrm e}^{2 x} \left (-\sin \left (2 x \right )+\cos \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 87
dsolve(1*diff(y(x),x$4)-8*diff(y(x),x$3)+32*diff(y(x),x$2)-64*diff(y(x),x)+64*y(x)=exp(2*x)*(cos(2*x)-sin(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{2 x} \left (4 x^{2}-6 x -41\right ) \cos \left (2 x \right )}{128}+\frac {{\mathrm e}^{2 x} \left (18 x^{2}+9 x -517\right ) \sin \left (2 x \right )}{576}+c_{1} \cos \left (2 x \right ) {\mathrm e}^{2 x}+c_{2} \sin \left (2 x \right ) {\mathrm e}^{2 x}+c_{3} \cos \left (2 x \right ) {\mathrm e}^{2 x} x +c_{4} \sin \left (2 x \right ) x \,{\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.199 (sec). Leaf size: 65
DSolve[1*y''''[x]-8*y'''[x]+32*y''[x]-64*y'[x]+64*y[x]==Exp[2*x]*(Cos[2*x]-Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{256} e^{2 x} \left (\left (-8 x^2+4 (1+64 c_4) x+5+256 c_3\right ) \cos (2 x)+\left (8 x^2+8 (1+32 c_2) x-1+256 c_1\right ) \sin (2 x)\right ) \]