Question

Find the derivatives dy/dx and d^2y/dx^2, and evaluate them at t = 2.

x=t^2 ,y = t ln t

Answer #1

Find d^2y/dx^2 . x = t^3 − 7, y = t − t^2
d^2y/dx^2=?

Evaluate ∫_0,3^2,4▒〖(2y+x^2 )dx+(3x-y)dy along〗 The parabola
x=2t, y=t^2 +3 Straight lines from (0,3) to (2,3) A straight line
from (0,3) to (2,4)

find dx/dx and dz/dy
z^3 y^4 - x^2 cos(2y-4z)=4z

compute partial derivatives df/dx and df/dy, and all second
derivatives of the function:
f(x,y) = [4xy(x^2 - y^2)] / (x^2 + y^2)

Use Green’s theorem to evaluate the integral: ∫(-x^2y)dx
+(xy^2)dy where C is the boundary of the region enclosed by y=
sqrt(9 − x^2) and the x-axis, traversed in the counterclockwise
direction.

Consider the system [ x' = -2y & y' = 2x] . Use dy/dx to
find the curves y = y(x).
Draw solution curves in the xy phase plane. What type of
equilibrium point is the origin?

Solve the following DE:
x dy/dx + 2y = x^2 - x + 1 ; y(1) = 1/2

find the particular solution for the following initial value
problems
A) x dy/dx +2y = x to the power of 2 +x , y(1)=1

(61). (Bernoulli’s Equation): Find the general solution of the
following first-order differential equations:(a) x(dy/dx)+y=
y^2+ln(x) (b) (1/y^2)(dy/dx)+(1/xy)=1

Find all the second-order partial derivatives of the following
function. w=(3x-4y)/(3x^2+y)
d^2w/dx^2
d^2w/dy^2
d^2w/dydx
d^2w/dxdy

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