Internal problem ID [1535]
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 38.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }-4 y={\mathrm e}^{x} \left (-\sin \left (2 x \right )+2 \cos \left (2 x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(1*diff(y(x),x$4)-3*diff(y(x),x$3)+2*diff(y(x),x$2)+2*diff(y(x),x)-4*y(x)=exp(x)*(2*cos(2*x)-sin(2*x)),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{x} \left (\frac {\cos \left (x \right )^{2}}{6}+\left (c_{3} -\frac {\sin \left (x \right )}{6}\right ) \cos \left (x \right )+c_{4} \sin \left (x \right )-\frac {1}{12}\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 56
DSolve[1*y''''[x]-3*y'''[x]+2*y''[x]+2*y'[x]-4*y[x]==Exp[x]*(2*Cos[2*x]-Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^{-x}+c_4 e^{2 x}+\frac {1}{12} e^x (\cos (2 x)-\sin (2 x))+c_2 e^x \cos (x)+c_1 e^x \sin (x) \]