1 du k at dx² d'u where his positive constant. : 00 Find the solution of IBVP: u(0,1)=0; u(1,1)+hu(1,1)=0, 1>0} u(x,0)=f(x): 0

Q: 2 (y – k) y' = 4a Find the Derivative - d/dy Since 4a is constant with respect to y, the derivative…

A: (1). The given expression is:2y-ky'=4a

Q: Vx6+7 (etan**) dy where ylny) = dx B) find (x2/3)( y v) sec

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Q: dy y = x-'(a² + x²)¿, solve for dx

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Q: 5. In rectangular coordinates verify that V · V x A = 0 where A = xyz(ê+ ŷ + 2) by carrying out the…

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Q: don't understand how the equation turned into 5x+x+6/x(x+6), could you go through the equation again…

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Q: Suppose u and v are differentiable functions of x. Use the given values of the functions and their…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Ex Find div F when F=3xyi+ 2xy3at (リ-1)

A: To find divergence of the given vector field at (1,-1)

Q: obtain the particular solutions satisfying the indicated conditions: dx/y=(25-x^2)^-1/2dy; y(0)=1

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Q: A 2xe ²x² B Xex² Ⓒ2e+² D 2xex² Let f(x)= ex², find f'(x)

A: given  f(x)=ex2d dx(ex)=exd dx(xn)=nxn-1

Q: dx 2. S; x²-4x+5

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Q: Find the area of each circle, given the radius r or the diameter d. Leave your answer in tems of t.

A: See the detailed solution below.

Q: 4. Find . d?y of the functions x = 1+ cost and y = 1– sin t. dx2

A: Differentiating given parametric equationswith respect to t,x=1+costdxdt=-sint…

Q: 1 X = (u +1)? dy ; y = u? + 3 -> dx

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Q: 1 Find h' (u). Show your work. Let h(u) = 4u³ – - u?

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Q: x2 sin3(x) Find ax if y = In \cos(x*).V1+x,

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Q: cy(1) = 4, y'′(1) = −2. y = x²y" +7xy +9y = xº,

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Q: dy – y (xy' -1) .3 2.) dx

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Q: Find whether the function F-(* - y')i + (v² – 3x)j + (=* - xy)k is irrotational.

A: A vector field F is called irrotational if curl (F) = 0.

Q: The given function  y = 9x3e−x  is of the form  y = uv,  where  u = 9x3  and  v =  e−x       . Use…

A: So, y=uvthen product rule is ddxuv=dudx×v+u×dvdx

Q: S2-3x', x>2 Vx -2, х <2 а) g(x)-

A: The given function is gx=2-3x3,   x&gt;2x-2,    x≤2. Sketch the graph of this function as shown…

Q: Find the quadratic approximation at (0,0) for f(x,y) = ln(1+x^2 + y^2).

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Q: Werify that (x)=- 1-ce* dy Substitute (x) for y and find the derivative to substitute for dx…

A: We have to verify that  where c is an arbitrary constant is a one parameter family of solution to

Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

A: