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 3 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)?

6. Consider the initial value problem dy/ dt = t ^2 y , y(1) = 1...

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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

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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

3. Consider the IVP: dy =ty^1/3; y(0)=0,t≥0. dt Both y(t) = 0, (the equilibrium solution) and...

3. Consider the IVP: dy =ty^1/3; y(0)=0,t≥0. dt Both y(t) = 0, (the equilibrium solution) and y(t) = ?(1/3t^2?)^3/2 are solutions to this IVP. (a) Show that the trivial solution satisfies the IVP by first verifying that it satisfies the initial condition and then verifying that it satisfies the differential equation. (b) Show that the other solution satisfies the IVP again by first verifying it satisfies the initial condition and then verifying that it satisfies the differential equation. (c) Explain...

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

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