Question

In: Advanced Math

Consider a nonhomogeneous differential equation ?′′ + 2?′ + ? = 2? sin? (a) Find any...

Consider a nonhomogeneous differential equation

?′′ + 2?′ + ? = 2? sin?

(a) Find any particular solution ?? by using the method of undetermined coefficients.

(b) Find the general solution.

(c) Find the particular solution if ?(0) = 0 and ?′(0) = 0.

Solutions

Expert Solution


Related Solutions

Find the general solution to the nonhomogeneous differential equation: y"-y=tsint
Find the general solution to the nonhomogeneous differential equation: y"-y=tsint
A. Find a particular solution to the nonhomogeneous differential equation y′′ + 4y′ + 5y =...
A. Find a particular solution to the nonhomogeneous differential equation y′′ + 4y′ + 5y = −15x + e-x y = B. Find a particular solution to y′′ + 4y = 16sin(2t). yp = C. Find y as a function of x if y′′′ − 10y′′ + 16y′ = 21ex, y(0) = 15,  y′(0) = 28, y′′(0) = 17. y(x) =
How do you find the complementary solution of a nonhomogeneous differential equation? Could someone give me...
How do you find the complementary solution of a nonhomogeneous differential equation? Could someone give me a general rule or few rules to find the complementary solution based on the appearance of the given equation or the roots of the given equation? Thanks
Solve the differential equation by variation of parameters. y''+ y = sin^2(x)
Solve the differential equation by variation of parameters. y''+ y = sin^2(x)
Consider the nonhomogeneous equation y"-8y'+16y=e^4x cos x. Find a particular solution of the equation by the...
Consider the nonhomogeneous equation y"-8y'+16y=e^4x cos x. Find a particular solution of the equation by the method undetermined coefficients.
Solve differential equation: y'+y=sin(x)
Solve differential equation: y'+y=sin(x)
(a) Write a general expression for yp(x) a particular solution to the nonhomogeneous differential equation [Do...
(a) Write a general expression for yp(x) a particular solution to the nonhomogeneous differential equation [Do not evaluate the coefficients] y′′ + 2y′ + 2y = e-x (4x + sin x) + 2 cos(2x). (b) Solve the initial value problem y′′ - y = 1 + 4ex; y(0) = 1; y′(0) = 2:
Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where...
Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where x=[x(t)y(t)]. x(t)= y(t)= please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most
Consider the differential equation y '' − 2y ' + 10y = 0;    ex cos(3x), ex sin(3x),...
Consider the differential equation y '' − 2y ' + 10y = 0;    ex cos(3x), ex sin(3x), (−∞, ∞). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. The functions satisfy the differential equation and are linearly independent since W(ex cos(3x), ex sin(3x)) = _____ANSWER HERE______ ≠ 0 for −∞ < x < ∞. Form the general solution. y = ____ANSWER HERE_____
Consider the differential equation y' = -18 + 11x - x2. (a) Find the equilibria (i.e....
Consider the differential equation y' = -18 + 11x - x2. (a) Find the equilibria (i.e. constant solutions). (b) By analyzing the sign of dy/dt around the equilibria, determine whether each equilibrium solution is stable, unstable, or neither. (c) Find an explicit general solution to the equation. (d) Graph the equilibrium solutions, as well as some non-constant solution curves, verifying visually the stability properties determined in (b).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT