We got for x > 0 given a differential equation y’ = 1-y/x,
with start value y(2)= 2
Find the Taylor polynomial of first and second degree for y(x)
at x =2.
Show that y(x) =x/2 +2/x solves the given equation.
Consider the differential equation
(x
2 + 1)y
′′ − 4xy′ + 6y = 0.
(a) Determine all singular points and find a minimum value for the
radius of convergence of
a power series solution about x0 = 0.
(b) Use a power series expansion y(x) = ∑∞
n=0
anx
n
about the ordinary point x0 = 0, to find
a general solution to the above differential equation, showing all
necessary steps including the
following:
(i) recurrence relation;
(ii) determination...
Let y(t) = (1 + t)^2 solution of the
differential equation y´´ (t) + p (t) y´ (t) + q (t) y (t) = 0
(*)
If the Wronskian of two solutions of (*) equals three.
(a) ffind p(t) and q(t)
(b) Solve y´´ (t) + p (t) y´ (t) + q (t) y (t) = 1 + t
Find the General Solutions to the given differential equations
y(t) =
a) 6y' +y = 7t^2
b) ty' − y =
9t2e−9t, t > 0
c) y' − 8y = 9et
d)
y' + y/t = 6 cos
5t, t
> 0