4) Solve Poisson problem for a=lı b=l ↑u (x₁b) = f₂(x) ty b (0₁4)=9₁(y) 0 Ou=f(x,y) u(a.y) = 9₂ (9) xx a u(x₁) = f(x) Figure 1. f(x,y) = sin2TX₁ f₁= £₂=0, 9₁=9₂=0 using one dimensional eigen function expansion. 1

Q: dx 1)y /sec(3x) 2) y = Vu + 2u , x= u? - 3u

A: Definition used -            Chain rule of derivative -                             ddx(f(g(x))=…

Q: 3) Find dy dx a) y = x+In(sec 3x) %3D In(x+)

A: solution:-

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A: We need to determine the volume of the torus: ρ=6sinφ.

Q: 1. Solve the following DE's (for y as a function of x, where possible): a) xy'= y – 2y, with y(1) =…

A:

Q: Find the derivatives of y with respect to x: a) y = xe* - e* b)' y = e(4x+) e(tx+) X. c) y = e*(sin…

A: Since you have posted multipart question and we can answer three subparts. So, answered first three…

Q: 8. Find the solution of the equation in the parametric form pq=xy, u(x, y) = -y when x = 0.

A:

Q: 1. If f(x, y)=3x' cos y– y sin x– 2.x In y- yln x-4x²y, find ôf ôf d²ƒ _ô²ƒ

A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In; x²+y

A: Given that a function f(x,y) is continuously differentiable on an open region, we can derive the…

Q: the derivatives of y with respect to x: y = xe* – ex y = e(1x+) %3D y = e*(sin x + cos x) %3D y =…

A:

Q: a) z=cos² (3 xy) onde x=p+eº ey=p²-2e³8 b) z=4x³y onde x=3p²+0² e y=p²-40²

A:

Q: -use newtors method to approximate a solution of the equation 5 Sin(x)-X=0 Set Xo = 1 be the initial…

A: We have to use Newton's method to approximate the solution of the equation5sin(x) - x = 0Also we…

Q: (a) y 10u² and u = 5 - ² (b) y = √u and u=1-1

A:

Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

A:

Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

Q: tind the derivatiues of given functions with respect tox. 12

A: Please refer to the image below

Q: Q4) Find the complete solution of the following equations: a) y" +3y' = sin x + 2 cos x (15)

A:

Q: Q2 Q2/If y = (x³ + 5x² + 1)3 + Jsin+/cos³Vtan3x2 find y'

A:

Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

Q: 6. Find the derivatives of the following: a) g(r) = sin(vi) dt %3D g(=) = /" Ve +4 dt

A: Please refer to the image below

Q: a) Find dy if y² + x²y² = 1+x^y use implicit differentiation b) If x² + y² = 6. Find y' in term OF…

A: