Solve the following initial value problem: tdy/dt+5y=5t with y(1)=8. Put the problem in standard form. Then...

Solve the following initial value problem: tdy/dt+5y=5t with y(1)=8.

Put the problem in standard form.

Then find the integrating factor, ρ(t)=

and finally find y(t)=

Expert Solution

This is the linear differential equation of first order of the standard form: (dy/dt) + P(t)y=Q(t). The integrating factor = e. The general solution is given by:

= . Then applying initial condition y(1)=8 we get the particular solution.

Colby Messinger answered 1 year ago

Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0)...

Solve the given initial-value problem. dx/dt = y − 1 dy/dt = −6x + 2y x(0) = 0, y(0) = 0

Solve the following initial value problem. y(4) − 5y′′′ + 4y′′ = x, y(0) = 0, y′(0) ...

Solve the following initial value problem. y(4) − 5y′′′ + 4y′′ = x, y(0) = 0, y′(0) = 0, y′′(0) = 0, y′′′(0) = 0.

se the Laplace transform to solve the given initial-value problem. y'' − 6y' = 10e^5t −...

se the Laplace transform to solve the given initial-value problem. y'' − 6y' = 10e^5t − 5e^−t, y(0) = 1, y'(0) = −1

Solve the following initial value problems (1) dy/dt = t + y y(0) = 1 so...

Solve the following initial value problems (1) dy/dt = t + y y(0) = 1 so y(t) = (2) dy/dt = ty y(0) = 1 so y(t) =

Solve the following initial value problem. x2y′′ + 19xy′ + 85y = 0, y(1) = 8, y′(1) ...

Solve the following initial value problem. x2y′′ + 19xy′ + 85y = 0, y(1) = 8, y′(1) = 6

Solve the given initial-value problem. y'' + 4y = −1, y(π/8) =3/4,y'(π/8) = 2 ,

8) Use the Laplace transform to solve the given initial-value problem. y' − y = 2...

8) Use the Laplace transform to solve the given initial-value problem. y' − y = 2 cos(4t), y(0) = 0 y(t)=??? 9) Use the Laplace transform to solve the given initial-value problem. y'' − 5y' = 8e4t − 4e−t, y(0) = 1, y'(0) = −1 y(t)=? 10) Use the Laplace transform to solve the given initial-value problem. y''' + 2y'' − y' − 2y = sin(4t), y(0) = 0, y'(0) = 0, y''(0) = 1 y(t)=?

10. Solve the following initial value problem: y''' − 2y '' + y ' = 2e...

10. Solve the following initial value problem: y''' − 2y '' + y ' = 2e ^x − 4e^ −x y(0) = 3, y' (0) = 1, y''(0) = 6 BOTH LINES ARE PART OF A SYSTEM OF EQUATIONS

Initial value problem : Differential equations: dx/dt = x + 2y dy/dt = 2x + y...

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...

Consider the following initial value problem dy/dt = 3 − 2t − 0.5y, y (0) =...

Consider the following initial value problem dy/dt = 3 − 2*t − 0.5*y, y (0) = 1 We would like to find an approximation solution with the step size h = 0.05. What is the approximation of y(0.1)?

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