Question

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

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

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 →∞

Solve the initial-value problem. y"-6y'+9y=0; y(0)=2,
y'(0)=3
Given that y1=x2 is a solution to y"+(1/x)
y'-(4/x2) y=0, find a second, linearly independent
solution y2.
Find the Laplace transform. L{t2 *
tet}
Thanks for solving!

Find y(t) solution of the initial value problem
3ty^2y'-6y^3-4t^2=0, y(1)=1, t>0

Find the solution of the given initial value problem:
y(4)+2y′′+y=5t+2; y(0)=y′(0)=0, y′′(0)=y'''(0)=1

Use Laplace transforms to solve the given initial value
problem.
y"-2y'+5y=1+t y(0)=0 y’(0)=4

solve the given initial value problem y''-5y'+6y=0, y(0)=3/5,
y'(0)=1

Verify that the given function is the solution of the initial
value problem.
1. A) x^3y'''-3x^2y''+6xy'-6y= -(24/x) y(-1)=0 y'(-1)=0
y''(-1)=0
y=-6x-8x^2-3x^3+(1/x)
C) xy'''-y''-xy'+y^2= x^2 y(1)=2 y'(1)=5 y''(1)=-1
y=-x^2-2+2e^(x-1-e^-(x-1))+4x

Solve the given initial-value problem.
y''' + 6y'' +
9y' = 0, y(0) = 0,
y'(0) = 1, y''(0) = −6

Solve the given initial-value problem.
y'' + 5y' −
6y =
12e2x, y(0)
= 1, y'(0) = 1

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