Solve y''-y=e^t(2cos(t)-sin(t)) with initial condition y(0)=y'(0)=0

Expert Solution

Colby Messinger answered 1 year ago

Solve the differential equation Y’(t) = AY(t), with initial condition Y(0) = [1;0] (a 2x1 matrix);...

Solve the differential equation Y’(t) = AY(t), with initial condition Y(0) = [1;0] (a 2x1 matrix); where A = [ 9 , 5 ; -6 , -2 ]. Then, using Euler’s method with step size h=.1 over [ 0 , .5 ] fill in the table with header where the 2x1 matrix Yi is the approximation of the exact solution Y(ti) : t Yi Y(ti) ||Y(ti) – Yi ||

Solve the equation y'=5-8y with initial condition y'(0)=0

Solve the Following Equation: y'' + y' + y = asin(ωt), y(0) = 0 , y'(0)...

Solve the Following Equation: y'' + y' + y = a*sin(ω*t), y(0) = 0 , y'(0) = 0 Thanks

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t...

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}: y′′+4y={sin(πt) ,0, 0≤t<11≤t y(0)=0,y′(0)=0 Y(s)= ? Hint: write the right hand side in terms of the Heaviside function. Now find the inverse transform to find y(t). Use step(t-c) for the Heaviside function u(t−c) . y(t)= ?

y'' - y = e^(-t) - (2)(t)(e^(-t)) y(0)= 1 y'(0)= 2 Use Laplace Transforms to solve....

y'' - y = e^(-t) - (2)(t)(e^(-t)) y(0)= 1 y'(0)= 2 Use Laplace Transforms to solve. Sketch the solution or use matlab to show the graph.

y''(t)+(x+y)^2y(t)=sin(xt+yt)-sin(xt-y*t), y(0)=0, y'(0)=0, x and y are real numbers

y''(t)+(x+y)^2*y(t)=sin(x*t+y*t)-sin(x*t-y*t), y(0)=0, y'(0)=0, x and y are real numbers

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

Use Laplace transforms to solve the initial value problem: y''' −y' + t = 0, y(0)...

Use Laplace transforms to solve the initial value problem: y''' −y' + t = 0, y(0) = 0, y'(0) = 0, y''(0) = 0.

Solve the IVP by applying the Laplace transform:y''+y=sqrt(2)*sin[sqrt(2)t]; y(0)=10, y'(0)=0

solve y'' + 4y =6 sin (t);y(0) =6, y'(0)=0 using 1st laplace transforms, 2nd undertinend coefficent,...

solve y'' + 4y =6 sin (t);y(0) =6, y'(0)=0 using 1st laplace transforms, 2nd undertinend coefficent, and 3rd variation of parameters.

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