Question

a nonhomogeneous equation and a particular solution are given. Find a general solution for the equation y=2y+11tan³x,yₚ(x)=11/2 tanx. The general solution is y(x)= (Do not use d,D,e,E,i, or I as arbitrary constants since these letters already have defined meanings.)

Answer 1

The general solution of the nonhomogeneous equation y' = 2y + 11tan³x with the particular solution yπ(x)=11/2 tanx is y(x) = Ce²x + 11/2 tanx, where C is an arbitrary constant.

Step-by-step explanation:

The subject is Mathematics, specifically differential equations. To solve for the general solution of the given nonhomogeneous equation, one must understand that a general solution can be expressed as a sum of a homogenous solution and a particular solution. The provided equation y = 2y + 11tan³x has a typo, and it should probably be y' = 2y + 11tan³x, where y' denotes the derivative of y with respect to x.

The particular solution given is yπ(x)=11/2 tanx. To find the general solution, we need to find the solution to the homogeneous equation, y' - 2y = 0, which is of the form yh(x)=Ce²x, where C is an arbitrary constant.

The general solution is then the sum y(x) = yh(x) + yπ(x), giving us y(x) = Ce²x + 11/2 tanx.