a) Use Laplace transforms to solve the following initial value problem for a second order ordinary differential equation: dy dy + 3- + 2y = H(t – 2), t>0, dt dy (0) = 1 dt2 y(0) = 0, dt where H is the Heaviside step function.

Q: b) Use Laplace transform to solve the system of differential equations dr 4y, dt dy dt +x = y + 3e*,…

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Q: dy y = sin h(2t),given that Solve the differential equation using Laplace transform dt2 y(0) = 0,…

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Q: b) Use Laplace transform to solve the system of differential equations UTM dr UTM x = 4y, dt y+Bet…

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Q: III. Find the general solution to the following differential equation via Laplace transforms.…

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Q: b) Solve the following second order differential equation using Laplace transforms d²x with initial…

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Q: ). Solve the initial value problem: du dx X ди +(t+1)=u, t>0 dt u(x,0) = f(x)

A: Given IVP is  xux+(t+1)ut=u ......(1) u(x,0)=f(x)

Q: (c) d²x dx dt dt Ix-0 +6+25x=e* with x(0)=0, dx dt Ix=0 = 0.

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Q: (c) Use Laplace transforms to solve the system of differential equations. z" + y" = e", 2.r' + y" =…

A: Given system of equations are as follows

Q: Consider the differential equation = (y – 2)²(1– x) dy %3D

A: a. The 12 points in the given axes are -1, 2, 0, 2, 1, 2, -1, 1, 0, 1, 1, 1, -1, 0, 0, 0, 1, 0, -1,…

Q: Use the Laplace transform to solve the given system of differential e dx 4x + d³y dt3 = 12 sin(t) dt…

A: dxdt−4x+d3ydt3=12sintdxdt+2x−2d3ydt3=0x0=0, y0=0, y'0=0, y''0=0

Q: post office sells 4-cent sheep stamps and 2-cent sunset stamps. Cole bought 5 stamps spent exactly…

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Q: olve the differential equation using Laplace transform. dy +4+4y=e-2t dt y (0) = 1 y'(0) = 2 d²y dt²

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Q: 1. Solve for x(t) and y(t), given that x(0)=D4 and y(0)=3 dx dy + x + 4y = 10; a dt dt x(t) 2+2e cos…

A: Solution :-

Q: T/F: The function y(t) = Pert-rt is a soln to s differential equation dy/dt = ry where P and r are…

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Q: Example 4: Solve the following differential equation using Laplace transformation: d²y +y = t2 * e',…

A: Given 3dydt-3d2ydt2+y=t2×et

Q: d²y(t) + 4y(t) = 16t dt²

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Q: 94 A) Solve the following differential equation using Laplace transformation: d²y +4y= 16t .y(0) = 3…

A: Q4. A) Solve the following differential equation using Laplace transformation:,        and .

Q: Consider the following. d²x = t² dt² d²x - = 6t dt² x(0) = 4, x'(0) = 0, y(0) = 0, y'(0) = 0 Give…

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Q: (b). Solve the following partial differential equation by using Laplace transforms du du +=x, x>0,…

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Q: d²x dx +2 +x=1 dt²2 dt F(0) = F'(0) = 0

A: To solve a differential equation using Laplace transforms.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.