Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,932 users

Find the particular solution?

0 votes

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

asked Nov 26, 2014 in CALCULUS by anonymous

1 Answer

0 votes

The Differential Equation are dy/dt = x and dx/dt = 6x - 8y

Let us Consider

dy/dt = x      ..................Equation(1)

Apply derivative on both sides

image               ..............Equation(2)

Now let us consider dx/dt = 6x - 8y

image

image

This is in the form of second order linear differential Equation.

then general solution of differential equation is image where r 1 and r2 are the real roots of the differential equation

Let us consider a auxiliary equation as r² - 6r + 8 = 0

r² - 4r - 2r + 8 = 0

r(r - 4) -2(r - 4) = 0

(r - 4)(r - 2) = 0

r = 4, 2

Solution of the differential Equation is image.

image        ...................Equation(3)

Differentiate with respect to t

image            ..................Equation(4)

Given Initial values are x = 1 and y = -1 when t = 0

Substitute initial values (t = 0 and y = -1) in Equation(3)

image

image     ..................Equation(5)

Substitute initial values(x = 1) in Equation(1) then

dy/dt = x

dy / dt = 1

Substitute initial values(t = 0 and dy / dt = 1) in Equation(4)

image     ..................Equation(6)

Multiply Equation(5) by 2

image     ..................Equation(7)

Subtract Equation(7) from Equation(6)

image

Substitute the above value in Equation(5)

image

Therefore the solution of Differential Equation is image.

 

answered Nov 26, 2014 by Lucy Mentor

Related questions

asked Oct 18, 2017 in CALCULUS by anonymous
...