Given the heat equation, U₁=Uxx, 00 XX u(0,t)= u(2,t)=0, t≥0 u(x,0)=3x(2-x),

Q: Find y as a function of a if y(0)2, y'(0) = 3, "(0) = -13. y(x) = y″ − 4y″ − y′ + 4y = 0,

A: Given a differential equation:initial conditions are:

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: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: f(r, y, z) = sec='(9x + 3yz) f. = fy = f; =

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

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Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = <2, 5, 1> and initial…

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

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Q: f(«, у, 2) — sec (9г + 3уг) fa = | fy = f: = ||

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Q: Let f"(t) = 2t + sin t, f(0) = 1 and f'(0) = 2. Evaluate f(27).

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Q: Find the first derivative f(t)-4cos (t)-10tan(t) -1

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Q: S-* cos(x²)dxdy = Q2): Show that 1-y2 %3D 6.

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