Question

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.

Answer #1

it can be shown that y1=x^(−2), y2=x^(−5) and y3=2
are solutions to the differential equation x^2D^3y+10xD^2y+18Dy=0
on (0,∞)
What does the Wronskian of y1,y2,y3 equal?
W(y1,y2,y3) =
Is {y1,y2,y3} a fundamental set for x^2D^3y+10xD^2y+18Dy=0 on
(0,∞) ?

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

Let y1 and y2 be two solutions of the equation y'' + a(t)y' +
b(t)y = 0 and let W(t) = W(y1, y2)(t) be the Wronskian. Determine
an expression for the derivative of the Wronskian with respect to t
as a function of the Wronskian itself.

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.

3.
Find two linearly independent solutions of t^2y′′ + 5ty′ + 5y = 0,
t > 0 and calculate their Wronskian

Consider the differential equation t 2 y" + 3ty' + y = 0, t >
0. (a) Check that y1(t) = t −1 is a solution to this equation. (b)
Find another solution y2(t) such that y1(t) and y2(t) are linearly
independent (that is, y1(t) and y2(t) form a fundamental set of
solutions for the differential equation)

let
y1=e^x be a solution of the DE 2y''-5y'+3y=0 use the reduction of
order method to find a second linearly independent solution y2 of
the given DE

Find the function y1(t) which is the solution of 4y″+32y′+64y=0
with initial conditions y1(0)=1,y′1(0)=0.
y1(t)=?
Find the function y2(t) which is the solution of 4y″+32y′+64y=0
with initial conditions y2(0)=0, y′2(0)=1.
y2(t)= ?
Find the Wronskian of these two solutions you have found:
W(t)=W(y1,y2).
W(t)=?

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.

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 = ?????

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