Differential Equations Answers

Fourier cosine integral of f(x) is

A)

cos Ax ff(t)sina tdt da 0

d cos 2x ff(t) cos at dt da

B) cosax ff(t)sintdtdx

D) 25 fcos Ax f f(t)cos At dt da

(d^2 y)/〖dx〗^2 +2 dy/dx+5y=34cos2x

6n + 4 = 16, find the value of 5n - 7

X^3=a+bp

xdx+ydy=a²(xdy-ydx)/x²+y²

(D^2-D'^2-3D+3D')z=e^x-2y

A rectangular steel sheet is bounded by the axis x = 0, y = 0, x = a and y = b. The temperature along the edge x = 0 are kept at 100°C and other edges are at 0°C. Let u(x,y) denote the temperature satisfying the equation [15] + d^2u/dx^2 + d^2u/dy^2 = 0 Find the steady state temperature u(x, y), by assuming the solution to be of the form u(x, y) = (AePX + Be-px)(C cospy + D sin py).

Let L1 be the line in R3 with equation (x,y,z)=(1,0,2)+t(−1,3,4); t∈R

and let L2 be the line that is parallel to L1 and contains the point (1, −1, 3). Let V be the plane that contains both the lines L1 and L2.

(a) Find two vectors that are both parallel to the plane V but are not parallel to one another.

(b) Find a vector that is perpendicular to the plane V .

(c) Find an equation for the plane V .

(d) Find an equation for the line L3 that is perpendicular to the plane V and contains the point (1, −1, 4) .

Hint: Find a parametric equation for L3. Don’t try to find a Cartesian equation for L3.

Given the function

𝑔(𝑥) = 𝑥 𝐽1 (𝑥) − 𝐴 𝐽0(𝑥) with 𝐴 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ≥ 0,

determine 𝑔′, 𝑔 ′′ and 𝑔′′′ . Reduce all expressions to functions of 𝐽0(𝑥), 𝐽1(𝑥) and 𝐴 only.