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.

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Q: y"+2y+y=e³x + 4 cos(3x)

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Q: Consider the differential equation dy(t)/dt − ay(t) = B cos ωt + A sin ωt. We would like to find…

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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)

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Q: In topology, a coffee cup and a donut are both of genus

A: Genus is the number of holes of a surface.

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

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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…

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Q: 3. Is the solution of (D₁) convergent or divergent? Justify your answer.

A: Given That : Differential equation is  2x'(t)-8e-x(t)+5=0 ,x(0)=ln(4)y(t)=ex(t)-3 To Find :…

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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.