Question

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 →∞

Answer #1

ﬁnd the general solution of the given differential equation
1. y''−2y'+2y=0
2. y''+6y'+13y=0
ﬁnd the solution of the given initial value problem
1. y''+4y=0, y(0) =0, y'(0) =1
2. y''−2y'+5y=0, y(π/2) =0, y'(π/2) =2
use the method of reduction of order to ﬁnd a second solution of
the given differential equation.
1. t^2 y''+3ty'+y=0, t > 0; y1(t) =t^−1

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

For the initial value problem
• Solve the initial value problem.
y' = 1/2−t+2y withy(0)=1

solve the initial value problem y''-2y'+5y=u(t-2) y(0)=0
y'(0)=0

ﬁnd the solution of the given initial value problem
1. y''+y'−2y=0, y(0) =1, y'(0) =1
2. 6y''−5y'+y=0, y(0) =4, y'(0) =0
3. y''+5y'+3y=0, y(0) =1, y'(0) =0
4. y''+8y'−9y=0, y(1) =1, y'(1) =0

Solve the initial value problem y = 3x^2 − 2y, y(0) = 4

Solve the initial value problem y' = 3x^2 − 2y, y(0) = 4

Solve the following initial value problem.
y''-2y'+2y=4x+5. ; y(0)=3. and y'(0)=0

Solve the Initial Value Problem:
?x′ = 2y−x
y′ = 5x−y
Initial Conditions:
x(0)=2
y(0)=1

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=____.

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