Initial conditions to find system of equations, Mathematics

Assignment Help:

Solve the subsequent IVP.

y′′ + 11y′ + 24 y = 0

y (0) =0

 y′ (0)=-7

 Solution

The characteristic equation is as

r2 +11r + 24 = 0

( r + 8) ( r + 3) = 0

 Its roots are r1 = - 8 and r2 = -3 and then the general solution and its derivative is.

y (t ) = ce-8t  + c e-3t

 y′ (t ) = -8c1e -8t - 3c2e -3t

 Here, plug in the initial conditions to find the subsequent system of equations.

0 = y (0) = c1 + c2

-7 = y′ (0) = -8c1 - 3c2

Solving this system provides c1 = 7and c2 = - 7. The actual solution to the differential equation is so y (t ) = (7/5) e-8t  - (7/5) e-3t


Related Discussions:- Initial conditions to find system of equations

The width of a rectangle is 30.5% of its length, The width of a rectangle i...

The width of a rectangle is 30.5% of its length l. Write a formula for the area and perimeter of the rectangle in terms of l only

Parametric equations and curves - polar coordinates, Parametric Equations a...

Parametric Equations and Curves Till to this point we have looked almost completely at functions in the form y = f (x) or x = h (y) and approximately all of the formulas that w

Prove that the height of the center of the balloon, A round balloon of radi...

A round balloon of radius 'a' subtends an angle θ at the eye of the observer while the angle of elevation of its centre is Φ.Prove that the height of the center of the balloon is a

Geometry, a figure is made of a rectangle and an isosceles right triangle. ...

a figure is made of a rectangle and an isosceles right triangle. the rectangle has sides of 6 in. and 3 in. one of the short sides of the rectangle is also one of the legs of the r

What was the total cost of the copies, Mary made 34 copies at the local off...

Mary made 34 copies at the local office supply store. The copies cost $0.06 each. What was the total cost of the copies? Multiply 34 by $0.06 to ?nd out the total cost; 34 × $0

Compute the essential matrix and epipolar lines , 1. In Figure there are th...

1. In Figure there are three cameras where the distance between the cameras is B, and all three cameras have the same focal length f. The disparity dL = x0 - xL, while the disparit

Point-slope form, The next special form of the line which we have to look a...

The next special form of the line which we have to look at is the point-slope form of the line. This form is extremely useful for writing the equation of any line.  If we know that

Number sequence, what is the formula to find a sequence on a string of numb...

what is the formula to find a sequence on a string of numbers?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd