Question

Solve

2(x+2)y''+4y'+6/(x+2)y=5

Answer #1

Solve for undetermined coefficients:
y'''-y''-4y'+4y=5 - e^x +e^2x

Solve the following differential equations using inspection:
1) y”+4y=12
2) y””+4y”+4y=-20
3) (D^4 -4D^2)y=24
4) y”-y=x-1
5) D(D-3)y=4
6) (D^2+2D-8)(D+3)y=0
7) y”-y’-2y=18xe^(2x)

solve the following systems
x'=3x-y+2 , x(0)=1
y'=-4y , y(0) =2

Solve the initial value problem y''+4y'+4y=0, y(-1)=5,
y'(-1)=5

solve the IVP
y'' - 4y' - 5y = 6e-x, y(0)= 1, y'(0) =
-2

Let F(x,y) = x^2 +3xy+4y^2 −14. Solve the equation x^2 +3xy+4y^2
−14 = 0
by the quadratic formula for x in terms of y. Determine dx/dy when
y = 1.
Find the function y = f(x) for which F(x,f(x)) = 0 and f(2) = 1.
Determine f′(2). How is f′(2) related to the value of dx/dy that
you found above.

solve for x(t) and y(t):
x'=-3x+2y;
y'=-3x+4y
x(0)=0,y(0)=2

Solve by matrix method
x-y+2z=7
3x+4y-5z=-5
2x-y+3z=12

Use
Gaussian Elimination to solve and show all steps:
1. (x+4y=6)
(1/2x+1/3y=1/2)
2. (x-2y+3z=7)
(-3x+y+2z=-5)
(2x+2y+z=3)

Solve the IVP with Cauchy-Euler ODE: x^2 y''+3xy'+4y=0; y(1)=0,
y’(1)=−2

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