Question

In: Advanced Math

Consider the equation t^2 -y"-t(t+2)y'+(t+2)y=2t^3, (t>0). Given that y1(t)=t3, y2(t)=te^t are the two fundamental solutions of...

Consider the equation t^2 -y"-t(t+2)y'+(t+2)y=2t^3, (t>0). Given that y1(t)=t3, y2(t)=te^t are the two fundamental solutions of the corresponding homogeneous equation, find the general solution of the nonhomogeneous equation.

Solutions

Expert Solution

please give a rating if it was helpful... Thank you


Related Solutions

a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation...
a) The functions y1 = x^2 and y2 = x^5 are two solutions of the equation x^2 y ″ − 6 x y ′ + 10 y = 0. Let  y be the solution of the equation x^2 y ″ − 6 x y ′ + 10 y = 3 x^5 satisfyng the conditions y ( 1 ) = 0 and  y ′ ( 1 ) = 1. Find the value of the function  f ( x ) = y ( x )...
a) Verify that y1 and y2 are fundamental solutions of the given homogenous second-order linear differential...
a) Verify that y1 and y2 are fundamental solutions of the given homogenous second-order linear differential equation b) find the general solution for the given differential equation c) find a particular solution that satisfies the specified initial conditions for the given differential equation y'' - y = 0 y1 = e^x, y2 = e^-x : y(0) = 0, y'(0) = 5
Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0...
Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0 and y'(1) = 0. • One function in the fundamental set of solutions is y1(t) = t. Find the second function y2(t) by setting y2(t) = w(t)y1(t) for w(t) to be determined. • Find the solution of the IVP
Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0...
Consider the IVP t2y''−(t2 + 2)y' + (t + 2)y = t3 with y(1) = 0 and y'(1) = 0. • One function in the fundamental set of solutions is y1(t) = t. Find the second function y2(t) by setting y2(t) = w(t)y1(t) for w(t) to be determined. • Find the solution of the IVP
Solve the differential equation. y'' − 8y' + 20y = te^t, y(0) = 0, y'(0) =...
Solve the differential equation. y'' − 8y' + 20y = te^t, y(0) = 0, y'(0) = 0 (Answer using fractions)
Given the differential equation y’’ +5y’+6y=te^t with start value y(0) = 0 and y’(0). Let Y(s)...
Given the differential equation y’’ +5y’+6y=te^t with start value y(0) = 0 and y’(0). Let Y(s) be the Laplace transformed of y(t). a) Find an expression for Y(s) b) Find the solution to the equation by using inverse Laplace transform.
Suppose y1 = -6e3t - 6t2 and y2 = 4e-2t - 6t2 are both solutions of...
Suppose y1 = -6e3t - 6t2 and y2 = 4e-2t - 6t2 are both solutions of a certain nonhomogeneous equation: y'' + by' + cy = g(t). a. Is y = 12e3t - 4e-2t + 6t2 also a solution of the equation? b. Is y = -6t2 also a solution of the equation? c. Could any constant function y = c also be a solution? If so, find all possible c. d. What is the general solution of the equation?...
a) verify that y1 and y2 are fundamental solutions b) find the general solution for the...
a) verify that y1 and y2 are fundamental solutions b) find the general solution for the given differential equation c) find a particular solution that satisfies the specified initial conditions for the given differential equation 1. y'' + y' = 0; y1 = 1 y2 = e^-x; y(0) = -2 y'(0) = 8 2. x^2y'' - xy' + y = 0; y1 = x y2 = xlnx; y(1) = 7 y'(1) = 2
Find the general solution of y'' + 2(sech^2 t)y = 0 (1), given that y1 =...
Find the general solution of y'' + 2(sech^2 t)y = 0 (1), given that y1 = tanh t is a solution to (1)
The parametric equations x = x1 + (x2 − x1)t,    y = y1 + (y2 − y1)t...
The parametric equations x = x1 + (x2 − x1)t,    y = y1 + (y2 − y1)t where 0 ≤ t ≤ 1 describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). Use a graphing device to draw the triangle with vertices A(1, 1), B(4, 3), C(1, 6). Find the parametrization, including endpoints, and sketch to check. (Enter your answers as a comma-separated list of equations. Let x and y be in terms of t.)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT