Question

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

Answer #1

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.

Series Solutions Near a regular singular point:
Find two linearly independent solutions to the given differential
equation.
3x2y"-2xy'-(2+x2)y=0

Use a series centered at x0=0 to find the general solution of
y"+x^2y'-2y=0. Use a series centered at x0=0 to find the general
solution. Write out at least 4 nonzero terms of each series
corresponding to the two linearly independent solutions.

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

consider ivp given by x^2y" + 2xy' - 6y = 0 w/ y(1) = 1, y'(1) = 2
verify y(x) = x^2 and y(x) = x^-3 are solutions
use wronskian to show both y(x) above are linearly
independent
find unique solution to ivp

Consider the differential equation x^2y′′ − 3xy′ − 5y = 0. Note
that this is not a constant coefficient differential equation, but
it is linear. The theory of linear differential equations states
that the dimension of the space of all homogeneous solutions equals
the order of the differential equation, so that a fundamental
solution set for this equation should have two linearly fundamental
solutions.
• Assume that y = x^r is a solution. Find the resulting
characteristic equation for r....

find the solution:
y'''+2y''-5y'-6y=7t²
y(0)=1, y'(0)=3, y''(0)=-1

Differential Equation:
Determine two linearly independent power series solutions
centered at x=0.
y” - x^2 y’ - 2xy = 0

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

find the general solution.
1- y^6(4)+12y''+36y=0
2-6y^(4)+5y'''+7y''+5y'+y=0
3-y^(4)-4y'''+7y''-6y'+2y=0

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