3. у") - бу' () - 2у(t) %3 4 сos 2t- 4t3; у (0) — — 2,у'(0) — 3 4 cos 2t - 4t3; У (0) — — 2, у'(0) — 3

Q: у" +у%3D0.001t?, У (0) %3D 0, у'(0) %3D 1.5

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Q: (y? + 7xy + 16x²)dx + x?dy = 0 when x = 1, y = 1 .2 Е 1, у %3D 1

A: the given differential equation is: y2+7xy+16x2dx+x2dy=0 and the given condition is when x=1, y=1.

Q: 6) —— (y² + z²)u₂ +xzu₂ − xyu¸ = 0

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Q: use the laplace transform to solve

A: Hi! As per norm we will be answering only the first question since both of the solutions are long.…

Q: 6y'' + 5y" + y' = 0 y(0) = -2, y'(0) = 2, y'"(0) = 0 %3D

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Q: f(d) = e-2d d4

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Q: + dy-39 sin ax y co) y'o) =12

A: Laplace transferom for the differential equation

Q: v" + v' / (x-1)=x-1 Hint: consider y' as the dependent variable.

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Q: 6. Evaluate * y" + 9y = 0; y(0) = 2 , y'(0) = 9 2cos3t + 3sin3t 2cos3t + 9sin3t C. A. 3(cos3t +…

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Q: 2, then the conju

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Q: 2. x"(t) – 4x'(t) + 4x(t) = 4e²t; x(0) = –1, x'(0) = -4 %3D

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Q: 3s2 + 5s + 1 (s)= (s2 + 15s + 34) %3D

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Q: Solve the given ODE using Laplace Transform

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Q: x"(t) – 4x'(t) + 4x(t) = 4e2t; x(0) = -1,x'(0) = -4

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Q: y" (t) – 6y'(t) – 2y(t) = 4 cos 2t – 4t³; y(0) = -2, y'(0) = 3 %3D

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Q: a) y n + 2] = 4y[n+ 1] + 5y[n] given that y[0]= 1, y[1] = 2.

A: Note: According to the guidelines we are allowed to solve one question at a time. Please post rest…

Q: Solve for the laplace transformarion of the given function

A: the Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that…

Q: у"(С) — бу'(t) — 2y(€) = 4 cos 2t – 4t³; y(0) -2, y'(0) = = -

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Q: Simplify tan(t)cot(t) to a single trig function or constant with no fraction

A: To Simplify tan(t)cot(t) to a single trig function or constant with no fraction

Q: * - 10x + 9x = 5t, x(0) = -1, x(0) = 2

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Q: (S+ TT)²*

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Q: y" – 4y' + 3y = 6t – 8 ; y(0) = 0, y'(0) = 0 - -

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Q: Deduce the derived function for y = cot -¹x.

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Q: Considering: { y"(t) + ty'(t) + ky(t) = 0 y(0) = v (0) = t0, k is a positive even number. Find a…

A: The Laplace Transform of an IVP , y''(t)+Ay'(t)+By(t)=f(t) y(0)=a and y'(0)=b is given by,…