Internal problem ID [1541]
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 44.
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 }-5 y^{\prime \prime \prime }+13 y^{\prime \prime }-19 y^{\prime }+10 y-{\mathrm e}^{x} \left (\left (7+8 x \right ) \cos \left (2 x \right )+\left (8-4 x \right ) \sin \left (2 x \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 61
dsolve(1*diff(y(x),x$4)-5*diff(y(x),x$3)+13*diff(y(x),x$2)-19*diff(y(x),x)+10*y(x)=exp(x)*((7+8*x)*cos(2*x)+(8-4*x)*sin(2*x)),y(x), singsol=all)
\[ y \relax (x ) = \frac {3 \cos \left (2 x \right ) {\mathrm e}^{x}}{4}-\frac {\left (4 x^{2}+4 x +23\right ) {\mathrm e}^{x} \sin \left (2 x \right )}{16}+\frac {7 \,{\mathrm e}^{x}}{2}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{x} \cos \left (2 x \right )+c_{4} \sin \left (2 x \right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 2.36 (sec). Leaf size: 3689
DSolve[1*y''''[x]-5*y'''[x]+13*y''[x]-19*y'[x]-10*y[x]==Exp[x]*((7+8*x)*Cos[2*x]+(8-4*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
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