Solve the 1-dimensional heat equation problem. ди J²u = Ət მე2 ди ди (0, t) = (1,t) = 0, for t> 0 Əx მე u (x, 0) = f(x) = 54 cos (2πx) + 3 cos (6πx), for 0≤ x ≤ 1

Q: X = cos 2t, y = cos t, 0 <t< n

A: given x=cos2t and y=cost interval 0&lt;t&lt;π  dx/dt =d/dt(cos2t) dx/dt=-2sin2t And dy/dt=d/dt(cost)…

Q: Find the solution Py = ²84, u a 81² ul₁=0 = sin ³7.x, ди du |-o = x(1 − x) (0 < x < l), u(0, t) =…

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Q: Consider the equation ut = Uxx, 0 0. Suppose u(0, t) = 0, u(1, t) = 0. Suppose u(x, 0) = -3 sin(x) +…

A: The given equation is  ut=uxx ,0&lt;x&lt;1,t&gt;0. Boundary Condition: u(0,t)=u(1,t)=0. Also…

Q: Find general solution, y., and particular solution y, of the following: (only solve for coefficient…

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Q: Find az/ax and dz/dy. xyz + cos(xy) - 2y sin(x) + z² = 3 Find az/ax and dz/dy. exz ZX y

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Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

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Q: (b) y" – 2y' + 5y = eª cos 2x, y(0) = 2, y' (0) = –1.

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Q: 9y" + 25y = 0; y(37/10) = 0, y'(3x/10) = 3. %3D O a. y3-cos(음) O b. y = c cos(x) + cz sin() Oc…

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Q: 2 cost x - V3 cos 2T 3 11개 6 ㅁ플 2 26 3п 미플 오크 ㅠ 2 COS X = 0

A: we need to find out the solutions.

Q: Q.1) The general solution of the equation e' cos , is:

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Q: Solve. y" + 6y (v¹)³=0 a. v(x) = C₂e1*-6 C₁y+y³=C₂ + x b. C. (C₂-y)² + x² = C₁ d. y=C₂-In(C₁-x²) e.…

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Q: 21. y" - 2y + 5y = e* cos(2x).

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Q: Find the solution of with y(0) = 9 and y'(0) = 7. Y y" + 3y = 126 sin(3t) + 162 cos(3t)

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