Use Laplace transform to solve the partial differential equation: d²u du ди(x,0) t> 0, 0

Q: sin(t) dt , 1-4x 1+ t2 4 If f(x) then f' (x) =

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Q: consider the ODE y'=2y/x, y(x0)=y0 does it have a solutioon for i. x0=0 and y0/=0…

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Q: If iz'+z?-z+i=0, then show that z=1. 3

A: Given z3 + z2 -z + i =0 We have to show that z = 1 iz3 + z2 -z + i =0iz(z2+i) + (z2 + i) = 0(z2 + i)…

Q: Consider the DE y"+exy'+ (sinx) y = ex+2lny then the order of the DE is ✓ and it is

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Q: Solve the following differential equation by Laplace transform y"+y=√2sin (√21), y(0) = 6, y' (0) =0

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Q: Find r'(t). 13 r(t) = 3 cos (t)i + 5 sin (t)j + k %3D r'(t) %3D

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Q: 1. (a) Use differentials to find a decimal approximation of V119.

A: Given data is : 11913 Use differentials to find a decimal approximation.

Q: solve y"+y'-2y=0 ,y(0)=4,y'(0)a=1

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Y"+y=secxtanx By using differential operators Methode

A: Given: The given equation is y''+y=secx tanx

Q: Verify that the function u=e(-α^2)t sin x is a solution of the heat conduction equation ut = α2uxx

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Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=<t sin t+cos t,2t2,sin t -t cos y> Then vector is given by r→t=t sin t+cos…

Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: Hint: Use method of undetermined coefficient Solve using the differential operator D=d/dx y" - 2y' +…

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = <2, 5, 1> and initial…

Q: Find the Fourier transform of the function y(t) if y(t) satisfies the differential equation d°y_dy…

A: First note that:  F-1e-5ω=12π∫-∞∞e-5ωejωtdω                       =12π∫-∞0e5ωejωtdω+12π∫0∞e-5ωejωtdω…

Q: W = x =t' +7, y=cos(2t), z=4t COS

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Q: Solve y(x) for the Second Order ODE in parameter form: y"+7y'+10y=6e^3x

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Q: y"+y' = 0; y(0) = 0, y '(0) = 1 cost + sint t + cost + sint A) 1- e-t t-e-t O

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Q: 4. a) Find the general solutions of the following differential equations. Express the general…

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Q: Solve the IVP to three decimal places when =. Check that your answer satisfies the ODE as well as…

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Q: Determine if the point x = 0 is an ordinary point, a regular singular point, or an irregular…

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Q: C is the curve y = e® from (2, e²) to (0,1) and F = (x², -y), compute ſ, F-dr.

A: Given that, C is the curve y=ex from 2,e2 to 0,1 and F=x2,-y Then, F=x2,-y=x2,-ex So, F→=x2i^-exj^

Q: Sketch the direction fields for the differential equation y' = y − x = f (x, y), then sketch the…

A: What is Slope Field: Slope fields, also known as direction fields, are graphical depictions of the…