3. Sove: e* (p-1) + e4 p =0, dy where P= ada 2. %3D Hint! Let u= e* and = e29 given equation to a Clairaut equation. to transform the

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A: w=ln8x2-4y+5z3x=t12y=t23z=t-2The chain rule says dwdt=dwdxdxdt+dwdydydt+dwdzdzdt

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Q: Assume that after  months, butterflies’ populace  in 1000 is calculated as: f(w) = 12w + cos(16w) +…

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Q: 3. Use Laplace transform to solve the IVP y" + 9y = e', y(0) = 0, y'(0) = 0. %3D %3D

A: Laplace transferom, solve the intial value problem

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Q: Assume that after months, butterflies’ populace in 1000 is calculated as: f(w) = 12w + cos(16w)…

A: Given f(w) = 12w + cos(16w) +n * 100

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Q: Use the Laplace transform to solve the given initial-value problem. y' + 5y = e4t, y(0) = 2 %3D y(t)…

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Q: Suppose solving an equation by Laplace transform results in 6 s Y(s) = s² + 64° Evaluate y(").

A: y(s)=ℒ(6ss2+64) =-3(2si(8s)-π)sin(8s)-6cos(8s)ci(8s) y(π)=-3(2si(8π)-π)-6cos(8π)si(8π)

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Q: (1. 1. 1) Evaluate the integral (5xy + 22°) dx + 5xf dy + (12z + 1) dz. (0.0.0) (Hint. Try the path…

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Q: у"+ 2y' + 5у %3D0, у(0) — — 1, у'(0) %3D

A: We have to solve the initial value problem y''+2y'+5y=0,  y(0)=-1, y'(0)=6

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y"…

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Q: general solution (without Laplace Transform): dy dy +2+ 5y = 2e-t. dt dt2

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Q: 1. Given:[(4x + 3)²D? – 12(4x + 3)D, + 64]y = 16[(4x + 3)² sec²(In|4x +3|)], what special case is…

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Q: solve the equation by using Lapalce transform Y(s) = ( – s2 + 8s + 37 ) / ( s+2 ) (s2 + 8s + 25 )

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A: Solve using miscellaneous substitution

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Q: D. Multiple Choice 1. Given: [(4x + 3)²D² - 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec² (In|4x + 3)],…

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Q: Use Laplace transform to solve the initial value problem y" – 2y' +y = e", y(0) = 0, y (0) = 0. %3D

A: Given problem :

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Q: : 0s 0s n, Os zs 1, 6Vzs rs 6}. Let E= Compute y?e(x2+y?)³ dv•

A: Given that, Let E=r,θ,z : 0≤θ≤π, 0≤z≤1, 6z≤r≤6 compute ∬∫Ey2ex2+y22dV

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Q: Consider the Bernoulli I.V.P ry'- x²y" = y, y(1) =1. where n-5. Let v= y" be the substitution that…

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Q: %3D I+ ylz

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Q: se Laplace transform to solve the initial value problem y" – 2y' + y = e2t, y(0) = 0, y/(0) = 0. %3D…

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Q: The indicated Turi Is a solution of th1e given d merentiai equation. Ose iula (5) Tn Section 4.2…

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Q: 1. Given:[(4x + 3)²D? – 12(4x + 3)Dx + 64]y = 16[(4x + 3)² sec²(In|4x + 3|)], what special case is…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: 10. Use the method of Laplace transform to solve the initial value problem y" – 2ay + (a? +B²)y = 0,…

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Q: By using Laplace transform to solve y + y = cosht y (0) = 0, what would the particular solution be?…

A: the given equation is y'+y=cosh t  y(0)=0 taking Laplace of the given transform Ly'+y=Lcosh t…