Find the general solution of this ODE: d²y dy +2- +y=12e-t dt² dt The solution will be of the form: y(t) = Cy₁(t) + Dy₂(t) + yp(t)

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A: We have ∂2u∂x∂y=cosx cosy The initial conditions are ∂∂xux,π=x, uπ,y=2 cosy Integrate ∂2u∂x∂y=cosx…

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Q: Find the general and Singular Solution of the following differential equation ·P² 21 (41

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Q: Find general solutions 17. y" - 4y = -12x² + 6x-4; 18. y"+y+y = -13 sin(2x);

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A: We can solve this using given information We can solve this using definition of sequence and limit

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Q: 2. The heights of Susa, Ada, and Rhea were 155 cm, 158 cm, and 161 cm, respectively. What is the…

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: Question 2 Use Euler's method with step length h = 0.5 and determine an approximate value for y(3)…

A: Solution: Given,  y′= 2x+1 5y4+1   y(1)=0 h=0.5 Euler method: 1st iteration:…

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A: Given that,Radius of first tank=1 mRadius of second tank=0.5 mBottom of second tank is 2 m above the…

Q: 2. Suppose that z is a function of and y, and F(xz - y². zy - 2², yz - ²) = 0. Calculate and (Hint:…

A: Solution :

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A: Let us determine the equilibrium points and its type of the following system in the next steps.

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Q: Let A and B be sets. Prove that if A = B, then A+ = B+.

A: Given: A and B To find: Solution

Q: 1. The product of (5254)^143 and (14344)^143 under modulo 143 is congruent to ___. a. 98 b. 121 c.…

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Q: Using Bisection method find the solution of T g(x) = 2x - 3 sin =8 Use as initial values 3 <-T 2 2n…

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Q: Find the general Solution of the following PDES ди -5X -3x 17 9 = 2 ди +u, ucx;o) = ду + 2 е ax…

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Q: Find the solution to the following linear programming problem using the simplex method Max…

A: MAX (Z) = 4x1 + 3x2 + 2x3 subject to :     3x1 + 2x2 + 5x3 ≤ 23         2x1 + x2 + x3 ≤ 8…

Q: (a) (i) ◄ Q8 (b) char(Z₂ x Z7 X Z₁4) = 14 (c) Z₂ x Z7 x Z12 = Z14 × Z12

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Q: Suppose Cn is a segn of real numbers such that lim 1c₂1h exists and is non-zero. If the ROC h-00 of…

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Q: Σ[1] (b) Test for convergence or divergence for the series

A: We solve given series by limit comparison test

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Q: y 10 8 6 4 2 X -5 5 -24 Amazing work. Find the domain of the function. (Enter your answer using…

A: Solution :  Domain of the function is  (- ♾️ , 3] union [3, ♾️)

Q: -B-Let f:( M, (2),+)-(M₂(2), +..) be a function define by such that g[]=[ g( . € M₂(2). Is f is…

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Q: a) Show that F is conservative while G is not. b) Evaluate GdR, where C3 is defined by R(t) = tî +…

A: This is a problem of vector calculus.

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Q: Question 5. Given a metric spaceX,p> (a) If the sequence (rn)EN CX is convergent, show that it is…

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Q: + f(x) af -12 -4 4 -20 -1 12 20 X

A: Solution: f(x)=40≤x&lt;4-14≤x&lt;848≤x&lt;12 Period = 16 Fourier series:…

Q: Obtain using Jacob's method, all the eigen values and eigen vectors of the following matrices: (a) 1…

A: We see that the given matrix is symmetric, that is aij=aji∀i,j A=110.5110.250.50.252 The largest…

Q: Solve the given differential equation. All solutions should be found. dy 3x² - 9y - y³ dx 9x + 3xy²…

A: Consider a differential equation of the form Mx,ydx+Nx,ydy=0. If ∂M∂y=∂N∂x, then the differential…

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Q: Consider the sequence 4, 8, 16, 32, ... Give a closed formula for the nth term of the sequence (in…

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, a) + (2y-3')] + 7k…

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Q: Given the functions y = 5x − x2 and y = x. (Sketch the graph) Solve for the surface area of y=x fro…

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Q: X-2 Evaluate the integral (t³ Inti+ 3t³ sin (t) j+ k) dt. x(x+1)

A: Given the integral ∫t3lnt i→+3t3sint4 j→+x-2xx+1 k→dt

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Q: dy = f(y). dt The following problem involves an equation of the form Sketch the graph of f(y) versus…

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Q: 2. Evaluate dx da dx a. //== /1+√ √ √ √==√₁ C. -

A: As per our guidelines we are supposed to answer only first question. Kindly repost other parts in…

Q: st sketching at least three cross sections in each

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Q: (e) For any nonzero real number z, prove Σε 1- 1-z""

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Q: π Show x² x² + x² +1 4 √3 -∞0 4 Hint: x² + x² +1= (xª + 2x² +1) − x² = (x² +1)² −x² dx =

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