Solve the following PDEs for u(x, t) 1. ux + 3ux = 0, u(x,0) = e-x² -∞ < x <∞, t> 0

Q: Uncicied 9. x- 2(x- y) – ? ifx = 2, y = -2, and z = -3

A: Given : x2 - 2( x - y ) - z3  When x =2 , y = -2 , z =-3

Q: Ex 6. Find the points at which the given function f has a local extremum: (i) f(x)=x²-11 on I =…

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Q: √√3+ rdr then 0 (2)=√√3+230 I X

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Q: Obtain the general solution of y√(1+x^2)dx+ x√(1+ y²)dy = 0 using variable separable method.

A: solution is given below..

Q: ,2k 101. Let F(x) = 2k . k! k=0 (b) Show that y = F(x) is a solution of y" = xy' + y. y(0) = 1,…

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Q: ,(x) = (x-x+1) y'(x)+3y'(x)+9 y(x) = 5x' +1 true false

A: False

Q: Solve the following IVP: X' = AX + f(t), where 2 -1 A = 3 -2 and X(0) = ( : -3 2 f(t) 10t ||

A: First we need to find the eigenvalues and eigenvectors of a then find the complementary solution of…

Q: 3(3y² + x²)dy - 2xydx = 0 when x = 3, y = -2

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Q: The quadratic approximation at x = 1 to f(x) is Q\left(x\right)=10+3\left(x-1\right) 3 (x – 1) + 2(x…

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Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: 4.z=(y'-2) 3/4-2y ;z= dz dy

A: The given equation is z=y3-24-2y3 The objective is to find dzdy. The product rule for derivates is…

Q: Solve the following ODE 2x y'- ( 1+x² у 0 with initial condition y(0) = 3 -

A: We have to solve

Q: Show that f(x) = x³ − x² − 3x + 1 has a zero over the interval [0, 1].

A: given function We need to sow that function has a zero on given interval.

Q: Let f (x)  =  { 8x x  ≤  12 −4x + 144 x  >  12 Evalute  36 ∫ 0f (x) dx.

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Q: If s = (x² + 1)²/3 (3y² + 8y +4) 4(3z+2) 5, find d²s d²s dy² d²s dz²

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Q: 8) A rational function has a HA at y = 2, an x -int of a VA at x = -4 and a y-int of - 3 Determine…

A: Given that the VA is x=-4, this means the denominator has a factor= (x+4) Given that the x-int is…

Q: Sa cos(r) dr = ,2 %3D 1 sin(r³) +c cos(r³) + c -1 - sin(r*) + c 3 cos(r³) + c 3 1/3

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Q: State the maximum interval over which the solution  is valid.

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Q: Given the preconditions for x and y as |x – y| ≤ 200, |2x + y - 150| ≤ 250, show the post-conditions…

A: Given that, z=3x2+y2+3xy-7x-8y+10 Subject to  x-y≤200 2x+y-150≤250

Q: b) Solve ди Ət ди +3x = 1+u, Әх -8AHAB, u(x,0) = f(x). t > 0,

A: Given pde is  ∂u∂t+3x∂u∂x=1+u,  -∞&lt;x&lt;∞, t&gt;0 and u(x,0)=f(x) we have to solve this pde

Q: x²-2x* 5. Integrate with respect to x x4

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Q: Consider the following functions. (x) = 2 + x, f,(x) = x, f;x) = x² g(x) = c,f,(x) + cof2(x) +…

A: A set of vectors {v1,v2,...,vk } is linearly independent if the vector equation x1v1+x2v2+···+xkvk…

Q: If f(x) = 12sin(green wave), then the red wave isni %3D 20 |-31/2 |-T1/2 T/2 3h/2 2n 5T -10

A: Solution A sinusoidal wave can be represented as f(x)=Asin(2πfx+P)..........(1) Where A is amplitude…