Q1) Solve the BVP ut = Uxx+sin 2x, 00 u(0,t) = 0, u(π, t) = 0 u(x,0) = 0

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

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Q: f= x? + क) | + ला (i) of =? (üi, af मु] liv) of

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Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: Verify whether yı = 3t4 and y2 = 4 t-2 form a fundamental set of solutions for f y" +7t y' + 8 y =…

A: We will verify the given statement.

Q: Prove using the IVT cosx = cos-1x has a solution in (0, 1).

A: cos x = x   rearrange to x - cos x = 0

Q: y"+y = sin x, use Method I

A: Given that: y''+y=sinx

Q: Determine exact solutions for the equation 2sin'x – 3sinx +1 = 0 in the interval xI [a, 3n].

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Q: All Sections 1) Solve the following equations for t Jy evt = 2) Find the derivative of y with…

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Q: W = spanR{1, cos² (x), sin² (x)} = R + Rcos² (x) + Rsin²(x) Justify for each of the subsets {1, cos²…

A: Given: W=spanℝ1, cos2x, sin2x=ℝ+ℝ cos2x+ℝ sin2xWe need to justify for each given subsets that it is…

Q: The equations xy² + 8xzcos(u) + ye" = 16 and xyz + xev – 9u?v² = 27 are solved for u and v as…

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Q: xy2 y' = ey + sin y dy = dx x+y y' = x2

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Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

Q: 2) x + xy+y -7= 0, (1,2) Ans. -4/5

A: We have, X^2 + xy + y^2 - 7 = 0 Differentiate with respect to x, we get 2x + [ x • dy/dx + y • dx/dx…

Q: f(x) = -12-21x + 18x^2 - 2.75x^3 what method will give a root of the function equal to - 0.287425 in…

A: We will use a numerical method to determine what will be the value of root of the given function in…

Q: Solve the following equation by using separation variable method: u(0,t)= u(6,t)=u(x,0)=0 u, (x,0)=…

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Q: poin If g(u) —D V9u + 3 then g' (u) =

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Q: 4) Let f(x) = - ax"+1 and a x) = 4X-3 5:) f(x) = Fxan? find the 3 first f,g and h. uch that (fo gohl…

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Q: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

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Q: If u = x3 -3xy and v= 3x2y-y3, prove that Pu/Əx2 + Pu/əy2 = Pv/ax2 + Pv/@y²

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Q: au at a²u 28. Solve Əx² U(x, 0) = 3 sin 2+x, U(0, t) = 0, U(1, t) = 0. = where 0 0 together with…

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Q: Solve the equation Ut u(0, t) u(4, t) u(x, 0) - = 2urr 3 -5 = 2

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Q: Let i be the unit imaginary number. Thus i2 = -1. (1) Observe that the usual algebra rule to…

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Q: [." T 0 15 30x-x² 9√x²+y² dydx =

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Q: Find Domain and Range бяц tue Ⓒsin (x+3) +2y x²+2y 3x + y² 3) 3x + Sin (3x) +2y+Z² Ⓒ x+2y cos2x…

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Q: +00 Find Ul-1/i, 1/i]. i=1

A: Given ∪i=1+∞−1i,1i First of all we will expand the union up to ∞.…

Q: e' [ S (5² +a²) 2 ] = t sinat 2a 7 Prove using Convolution

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Q: of of +y y Let f(x, y) = x$y² tan Then x equals X

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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: DON'T USE CHATGPT Solve the following equation by canceling operator y"+y = 3x sin(x) (In the answer…

A: First of all we find the auxiliary equation for the corresponding homogenous equation. Find the…

Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

Q: ) 3(x+ y) dx + x(x*+ zy + uy) dy - o t.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Solve J²u = Ət² u (0, t) = u (x, 0) = J²u 4- 2 მ2 u (π, t) = 0 sin (2x), 0 0 (x, 0) = 0 Ju Ət

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Q: Write the differential equation and then determine whether you have overdamped,critically damped,or…

A: Introduction: The differential equation of motion of an unforced damped harmonic oscillation is…

Q: x = s·t u = x² + y³ +z*, {y = s² +² z = s- t

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Q: The equations ry² + 8xzcos(u) + ye® = 16 and x³yz + xe" – 5u²v² = 15 are solved for u and v as…

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Q: Use the method of Characteristic to solve U t tuux = 2t, u(x, 0) = 3x.

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Q: Solve as simply as possible: J²u Ət² with u(a, , t) = 0, u(r, 0, 0) = 0, and 9 (r, 0, 0) = a(r) sin…

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Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

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