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) =

Expert Solution

milcah answered 2 years 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

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)?

Consider the system modeled by the differential equation dy/dt - y = t with initial condition y(0) = 1

Consider the system modeled by the differential equation dy/dt - y = t with initial condition y(0) = 1 the exact solution is given by y(t) = 2et − t − 1 Note, the differential equation dy/dt - y =t can be written as dy/dt = t + y using Euler’s approximation of dy/dt = (y(t + Dt) – y(t))/ Dt (y(t + Dt) – y(t))/ Dt = (t + y) y(t + Dt) =...

Use a LaPlace transform to solve d^2x/dt^2+dx/dt+dy/dt=0 d^2y/dt^2+dy/dt-4dy/dt=0 x(0)=1,x'(0)=0 y(0)=-1,y'(0)=5

Solve the following initial value problems y'' + y = 2/cos x , y(0) = y'(0)...

Solve the following initial value problems y'' + y = 2/cos x , y(0) = y'(0) = 2 x^3 y''' − 6xy' + 12y = 20x^4, x > 0, y(1) = 8/3 , y'(1) = 50/3 , y''(1) = 14 x^2 y'' − 2xy' + 2y = x^2, x > 0, y(1) = 3, y'(1) = 5

solve the following initial value problem y''+4y'=g(t),y(0)=0,y' (0)=1 if g(t) is the function which is 1...

solve the following initial value problem y''+4y'=g(t),y(0)=0,y' (0)=1 if g(t) is the function which is 1 on [0,1) and zero elsewhere

Solve the laplace transform to solve the initial value problem. y"-6y'+9y=t. Y(0)=0, y'(0)=1

Solve the following initial value problem d2y/dx2−6dy/dx+25y=0,y(0)=0, dy/dx(0)=1.

Use Laplace transformations to solve the following differential equations: dy(t)/dt + a y(t) = b; I.C.s...

Use Laplace transformations to solve the following differential equations: dy(t)/dt + a y(t) = b; I.C.s y(0) = c d2y(t)/dt2 + 6 dy(t)/dt + 9 y(t) = 0; I.C.s y(0) = 2, dy(0)/dt = 1 d2y(t)/dt2 + 4 dy(t)/dt + 8 y(t) = 0; I.C.s y(0) = 2, dy(0)/dt = 1 d2y(t)/dt2 + 2 dy(t)/dt + y(t) = 3e-2t; I.C.s y(0) = 1, dy(0)/dt = 1

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...

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