Question

Solve the initial value problem y"+xy'+y'-y=0, y(0)=1, y'(0)=0, and then find a pattern for the terms so you can write the solution in Infinite Sum form

Answer #1

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Find the first five nonzero terms in the solution of the given
initial value problem.
y′′−xy′−y=0, y(0)=5, y′(0)=8
Enter an exact answer.

Find the first five nonzero terms in the solution of the given
initial value problem.
y′′+xy′+2y=0, y(0)=5, y′(0)=9
Differential Equations

Solve the initial value problem below.
x2y''−xy'+y=0, y(1)=1, y'(1)=3
y=

Solve the following initial value problem: x2y′′+xy′−9y=0; y(1)
= 6; y′(1) = 12

For 2y' = -tan(t)(y^2-1) find general solution (solve for y(t))
and solve initial value problem y(0) = -1/3

Solve the initial value problem (xy' = 2y + x^ 3 + 1, y(1) =
1/2, x > 0

Solve the Initial Value Problem:
a) dydx+2y=9, y(0)=0 y(x)=_______________
b) dydx+ycosx=5cosx,
y(0)=7d y(x)=______________
c) Find the general solution, y(t), which solves the problem
below, by the method of integrating factors.
8t dy/dt +y=t^3, t>0
Put the problem in standard form.
Then find the integrating factor, μ(t)= ,__________
and finally find y(t)= __________ . (use C as the unkown
constant.)
d) Solve the following initial value problem:
t dy/dt+6y=7t
with y(1)=2
Put the problem in standard form.
Then find the integrating...

Solve the Initial Value Problem:
dydx+2y=9,
y(0)=0
dydx+ycosx=5cosx,
y(0)=7d
Find the general solution, y(t)y(t), which solves the problem
below, by the method of integrating factors.
8tdydt+y=t3,t>08tdydt+y=t3,t>0
Put the problem in standard form.
Then find the integrating factor,
μ(t)=μ(t)= ,__________
and finally find y(t)=y(t)= __________ . (use C as the
unkown constant.)
Solve the following initial value problem:
tdydt+6y=7ttdydt+6y=7t
with y(1)=2.y(1)=2.
Put the problem in standard form.
Then find the integrating factor, ρ(t)=ρ(t)= _______ ,
and finally find y(t)=y(t)= _________ .

Solve the initial value problem xy′ +2y = e^x2 , y(1) = −2

Solve the initial value problem y''−y'−2y=0, y(0) = α, y'(0) =2.
Then ﬁnd α so that the solution approaches zero as t →∞

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