Question

Given that y1 = t, y2 = t 2 are solutions to the homogeneous version of...

Given that y1 = t, y2 = t 2 are solutions to the homogeneous version of the nonhomogeneous DE below, verify that they form a fundamental set of solutions. Then, use variation of parameters to find the general solution y(t).

(t^2)y'' - 2ty' + 2y = 4t^2 t > 0

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The function y1(t) = t is a solution to the equation. t2 y'' + 2ty' -...
The function y1(t) = t is a solution to the equation. t2 y'' + 2ty' - 2y = 0, t > 0 Find another particular solution y2 so that y1 and y2 form a fundamental set of solutions. This means that, after finding a solution y2, you also need to verify that {y1, y2} is really a fundamental set of solutions.
The nonhomogeneous equation t2 y′′−2 y=29 t2−1, t>0, has homogeneous solutions y1(t)=t2, y2(t)=t−1. Find the particular...
The nonhomogeneous equation t2 y′′−2 y=29 t2−1, t>0, has homogeneous solutions y1(t)=t2, y2(t)=t−1. Find the particular solution to the nonhomogeneous equation that does not involve any terms from the homogeneous solution.
In this problem verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation....
In this problem verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation. Then find a particular solution of the nonhomogeneous equation. x^2y′′−3xy′+4y=31x^2lnx, x>0, y1(x)=x^2, y2(x)=x^2lnx. Enter an exact answer.
The nonhomogeneous equation t2 y′′−2 y=19 t2−1, t>0, has homogeneous solutions y1(t)=t2, y2(t)=t−1. Find the particular...
The nonhomogeneous equation t2 y′′−2 y=19 t2−1, t>0, has homogeneous solutions y1(t)=t2, y2(t)=t−1. Find the particular solution to the nonhomogeneous equation that does not involve any terms from the homogeneous solution. Enter an exact answer. Enclose arguments of functions in parentheses. For example, sin(2x). y(t)=
Given y1(t)=t^2 and y2(t)=t^-1 satisfy the corresponding homogeneous equation of t^2y''−2y=2−t3,  t>0 Then the general solution to...
Given y1(t)=t^2 and y2(t)=t^-1 satisfy the corresponding homogeneous equation of t^2y''−2y=2−t3,  t>0 Then the general solution to the non-homogeneous equation can be written as y(t)=c1y1(t)+c2y2(t)+yp(t) yp(t) =
Show that the given functions y1 and y2 are solutions to the DE. Then show that...
Show that the given functions y1 and y2 are solutions to the DE. Then show that y1 and y2 are linearly independent. write the general solution. Impose the given ICs to find the particular solution to the IVP. y'' + 25y = 0; y1 = cos 5x; y2 = sin 5x; y(0) = -2; y'(0) = 3.
Two solutions to the differential equation y00 + 2y0 + y = 0 are y1(t) =...
Two solutions to the differential equation y00 + 2y0 + y = 0 are y1(t) = e−t and y2(t) = te−t. Verify that y1(t) is a solution and show that y1,y2 form a fundamental set of solutions by computing the Wronskian
given that y1=xcos(lnx)and y2=xsin(lnx)form a fundamental set of solutions to x^2y''-xy'+2y=0,find general solution to x^2y''-xy'+2y=xlnx
given that y1=xcos(lnx)and y2=xsin(lnx)form a fundamental set of solutions to x^2y''-xy'+2y=0,find general solution to x^2y''-xy'+2y=xlnx
Consider the differential equation: 66t^2y''+12t(t-11)y'-12(t-11)y=5t^3, . You can verify that y1 = 5t and y2 =...
Consider the differential equation: 66t^2y''+12t(t-11)y'-12(t-11)y=5t^3, . You can verify that y1 = 5t and y2 = 4te^(-2t/11)satisfy the corresponding homogeneous equation. The Wronskian W between y1 and y2 is W(t) = (-40/11)t^2e^((-2t)/11) Apply variation of parameters to find a particular solution. yp = ?????
if y1 and y2 are linearly independent solutions of t^2y'' + 3y' + (2 + t)y...
if y1 and y2 are linearly independent solutions of t^2y'' + 3y' + (2 + t)y = 0 and if W(y1,y2)(1)=3, find W(y1,y2)(3). ROund your answer to the nearest decimal.