= function given by llowing heat equation. du at 0x² 1₁ f(x) = X₂ if 0 ≤ 2-x, if1< u(0, 1) = u(2, 1) = 0,

Q: √²³₁(−12xy² + 8x³y + 3)dxdy

A: LetWe have to evaluate the above integral.

Q: Differentiate the function. f'(x) = f(x) = e5

A:

Q: 3. If f(x) = sinx ex find f'(0).

A: fx=sinxex

Q: Determine the values of the constants a and b which make the function f(x) below continuous at x =…

A: A function f(x) is continous at x = a when:

Q: b.) If r(x)= 1 √g(2x) > find r'(x) at x = 2

A: Topic = Derivative

Q: Find y as a function of a if y(1) = -4, y'(1) = -9. y x²y" + 2xy' - 6y = 0,

A:

Q: * Find y as a function of æ if y" – 8y" – y' + 8y = 0, y(0) = 4, y'(0) = -6, y" (0) = 130. y(x) =

A:

Q: Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

A: y′′′+36y′=0y(0)=6,y′(0)=24,y′′(0)=108.The characteristic equation…

Q: Find the function satisfying y' x + 3 and y(0) = 2 ... 2y + 5

A:

Q: Find y as a function of t if 25y"- 70y' + 53y = 0, and y(5) = 8, y'(5) = 1. %3D y = %3D

A: Given: 25y''-70y'+53y=0  with the IVP y(5)=8 ,    and   y'(5)=1By…

Q: Apply variation of parameters to find a particular solution of y ''' - y' = tan x

A: The given differential equation is y''-y' = tan x.We have to solve this using the variation of…

Q: ) Find y as a function of x if x?y" + 2xy' – 42y = 0, y(1) = 5, y'(1) =-3. y =

A:

Q: Find all possible functions with the given derivatives. a. y' = 2x b. y' = 2x - 5 c. y'= 3x² - 2x -…

A: a y'=2x           b y'=2x-5           c y'=3x2-2x-5

Q: A function H is differentiable at x = 2. An equation for the line tangent to the graph of H at x = 2…

A:

Q: d Suppose that f(x) and g(x) are differentiable functions such that f(5) = 1, f'(5) = 7, g(5) = 2,…

A: The objective is to simplify the given differential equation.