Let us solve the following equation via separation of variables du(x, t) Ət = 3 Pu(x, t) dx² a) After using the ansatz u(x, t) = X(x)T(t), which equations do you get? Pick only two. (below C' denotes a constant) 3T (t) JT(1) = 1T(t) JT (1) de = 3CT(t) 0³X(x) d² CX(x) ²X(z) Dz² √C X(x) D De 8² X(z) = X(x) = = = √3CT(t)

Q: Find the derivative. x10 12) y = cos /t dt

A: We differentiate both sides with respect to x

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A: The given function is  y=3x3-4x2+5+x3-2x5x2y=3x3-4x2+5+x13-2x52x2

Q: Differentiate: y= 5 cot2 (25r) Oy = 750z cot2 (25r) csc(25z) CSC Oy=-750z cot (25r) csc (25z) O…

A:

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A: Given data:The rate of change of the volume V(t) of blood in the aorta at time t is given by…

Q: dy Find , for the implicit function 7 x²y³ + 2 x² = 3xy. dx

A:

Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

A:

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A: The solution is given as

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A:

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A: y= x^2 - 2x + 3

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A: Consider the equation

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A: Solution: Given:    Width is one third of the length of rectangle     and the perimeter of rectangle…

Q: dy Find by implicit differentiation. dx 8x - 13xy+5y = 32

A: 8x2-13xy+5y2=32diffrentiate by chain and product rule16x-13(y+xy')+10yy'=0