Question

(x+1)y'=y-1 2) dx+(x/y+(e)?)dy=0 3)ty'+2y=sint 4) y"-4y=-3x²e3x 5) y"-y-2y=1/sinx 6)2x2y"+xy'-2y=0 ea)y=x' b) x=0 2dx/dt-2dy/dt-3x=t; 2

Answer #1

dx
dt
= y − 1
dy
dt
= −3x + 2y
x(0) = 0, y(0) = 0

find dy/dx
a. (x+y)^4 =4y-9x
b. y= (x +6)^2x
c. y= cos^-1 (3x^2 -5x +1 )

Solve the following:
(3x^2 - y^2)dx + (xy - x^3y^-1)dy = 0

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

Use the Laplace transform to solve the given system of
differential equations. dx/dt=x-2y dy/dt=5x-y x(0) = -1, y(0) =
6

solve the given initial value problem. y(cos2t)e^ty -
2(sin2t)e^ty + 2t + (t(cos2t)e^ty - 3) dy/dt = 0, y(0)=0

Solve the initial value problems.
1) x (dy/dx)+ 2y = −sinx/x , y(π) = 0.
2) 3y”−y=0 , y(0)=0,y’(0)=1.Use the power series method
for this one . And then solve it using the characteristic
method
Note that 3y” refers to it being second order
differential and y’ first

Initial value problem : Differential equations:
dx/dt = x + 2y
dy/dt = 2x + y
Initial conditions:
x(0) = 0
y(0) = 2
a) Find the solution to this initial value problem
(yes, I know, the text says that the solutions are
x(t)= e^3t - e^-t and y(x) = e^3t + e^-t
and but I want you to derive these solutions yourself using one
of the methods we studied in chapter 4) Work this part out on paper
to...

3. Consider the equation (3x^2y + y^2)dx + (x^3 + 2xy + 5)dy =
0. (a) Verify this is an exact equation
(b) Solve the equation

dy/dt=x , dx/dt=6x-8y, x=1 and y=-1 when t=0

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