Use Laplace Transforms to solve the following differential equation. y - ay = f(t), y(0) = 4 is a constant f(t-r)e dr y(t) = ae" + 4t | y(t) = 4et + f(t-T)e dr y(t) = eat + f(7) sin 47dr y(t) = 4et + f(t - T) sin 47dT O None of the given choices

Q: For which of the following differential equations are the slopes at points on a vertical line t = C…

A:

Q: Find the differential of each function.

A:

Q: ay 1. Consider the differential equation dt The solution to this differential equation models the…

A: dydt=yt2+1⇒dydt=ftt2+1 So, the value of derivative at t=0 is  dydt=f00+1=2 Equation of tangent line…

Q: Solve the differential equation. dy y + 1 dx O In |x| – ? () = tan - ex - x + tan-'(x) = C In |x| –…

A:

Q: iCN Bf the following represents its different (a) = sin x (b) dx dy (c) =y- =ーツ (d) dr dy =x +y (e)…

A: Consider the curve in (a) dydx=sinx. In first quadrant, x>0,y>0. dydx=sinx>0 Therefore the…

Q: Give a recursive definition of the following sequences {a,}, n = 1,2, 3, ..... Put the appropriate…

A: We have to match the given recurring relation.

Q: ,2x Calculate the second derivatives of function f(x) = sin(x) + Ide²x at point x = 0.625 using…

A: Three point central differential formula for 2nd derivative   f′′(x)= f(x-h)-2f(x)+f(x+h)h2 Five…

Q: Q5) find the derivative 1. x = sin and y = sin+ cos if taken together, satisfy the differential…

A:

Q: Find the differential operator which will annihilate the function 2x + r³ – sin 2r.

A:

Q: (3) Using differentials, approximate the value of ₹28.3. Give your answer to 4 decimal places.

A: We are authorized to answer one question at a time, so we are answering the first question, please…

Q: Write the first-order differential equation in standard form. (Use yp for dy/dt.) dy dt = 7y + ty +…

A: The standard form of a first-order differential equation is dydt+g(t)y=h(t)or, y'+g(t)y=h(t)…

Q: v = ) V In(2x-3y

A:

Q: dy/dx=(x+2y-3)/(2x+y-3)

A:

Q: Verify that the indicated family of functions is a solution of the given differential equation.…

A:

Q: Find the differential of the function z=2x'y %3D

A: If z is a function of two variables defined by z=f(x,y) then the differential dz or total…

Q: dy Consider the differential equation - 2r da (A) At the point (1, -1), the direction field has a…

A: This question can be solved using the concept of direction field.

Q: (1 point) Find the differential of the function w = dw dx+ = x³ sin(y526) dy+ dz

A:

Q: The standard form of the following linear differential equation sin x = (cos x)y + xsin x + 2 is: dx

A:

Q: convolution theorum, S -1) 12 šta

A:

Q: 1 - dt -dy=C %3D

A:

Q: Which of these differentials is exact? (only one of them is exact) (1 – 2xy)dx + (x² + y²) dy O (22…

A:

Q: Solve the ODE with differentials operator (D²+4)y= cos(2x) + cos (4x)

A: Linear ordinary differential equation

Q: (2^)u sec (VTt) 2V7t (a) y= tan dy: dt 5- v2 (b) y = 5 + v2 dy = -5- 2iv 5 -V-5-2iv5 %3D Need Help?…

A: Both the parts are given below.

Q: Use Laplace transformation technique to solve the differential equation. y’’ + 1 = 2t y(0)=2 y’(0)=1

A: Answer