Question

solve the boundary value problem:

y''(x)+y(x)=e^x for 0<x<pi with y(0)=0 and
y(pi)+y'(pi)=0.

please show all steps.

Answer #1

find the eigenvalues and eigenfunctions for the given
boundary-value problem.
y'' + (lambda)y = 0, y(-pi)=0, y(pi)=0
Please explain where alpha = (2n+1)/2 comes from in the
lambda>0 case. Thank you!!

Please show all steps, thanks!!
a) Solve the BVP: y" + 2y' + y = 0, y(0) = 1, y(1) =3
b) Prove the superposition principle: suppose that the functions
y1(x) and y2(x) satisfy the homogenous equation of order two: ay''
+ by' + cy = 0.
Show that the following combinations also satisfy it:
constant multiple m(x) = k*y1(x)
sum s(x) = y1(x) + y2(x)

Solve the initial value problem.
d^2y/dx^2= -3 csc^2 x; y' (pi/4)=0; y(pi/2)=0
The solution is y=____.

Solve the 1st order initial value problem:
1+(x/y+cosy)dy/dx=0, y(pi/2)=0

Solve the given boundary-value problem.
y'' − 2y' + 2y = 2x − 2,
y(0) = 0, y(π) = π

Solve the initial-value problem.
x2y' + 2xy = ln(x), y(1) =
7.
Please show all work neatly, line by line, and please justify
steps so that I can learn.
Thank you!

Solve the below boundary value equation
1. Ut=2uxx o<x<pi 0<t
2. u(0,t) = ux(pi,t) 0<t
3. u(x,0) = 1-2x 0<x<pi

Please show all steps to the first order equation, using
infinity series.
a) solve:
y' - y = 0
b) solve:
(x-3)y' + 2y = 0

Given: The following boundary value problem:
y"+ lamda*y = 0;
0 < x < 2; y(0) =
0; y’(2) = 0
Find corresponding eigenvalues, (lamda)n
and normalized eigenfunctions yn
Expand the function f(x) = x, in terms of the eigen functions
obtained in (i)

Please show all steps, using infinite series.
Solve the IVP:
y" - xy' - y = 0

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