(Solved): Suppose that a fourth order differential equation has a solution \( y=2 e^{4 x} x \sin (x) \). Find ...

Suppose that a fourth order differential equation has a solution \( y=2 e^{4 x} x \sin (x) \). Find such a differential equation, assuming it is homogeneous and has constant coefficients. \( y^{\wedge}(4)-16 y^{\wedge}(3)+98 y^{\wedge}(2)-272 y^{\wedge}(1)+289 y=0 \) help (equations) Find the general solution to this differential equation. In your answer, use \( c_{1}, c_{2}, c_{3} \) and \( c_{4} \) to denote arbitrary constants and \( x \) the independent variable. Enter \( c_{1} \) as "c1", \( c_{2} \) as "c2", etc: Enter the solution as an equation \( y= \) ?. 1elp (equations)