Question

find the total differential

(a) f(x,y)=x^2+3xy+2y

(b) f(x,y)=x-y/x+1

Answer #1

x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3
differential equation using the Cauchy-Euler method

x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3
differential equation using the Cauchy-Euler method

Consider the differential equation x^2y′′ − 3xy′ − 5y = 0. Note
that this is not a constant coefficient differential equation, but
it is linear. The theory of linear differential equations states
that the dimension of the space of all homogeneous solutions equals
the order of the differential equation, so that a fundamental
solution set for this equation should have two linearly fundamental
solutions.
• Assume that y = x^r is a solution. Find the resulting
characteristic equation for r....

Show that the function f(z) =x^3-3xy^2+i((3x^2y-y^3) is
differentiable

Find the absolute maximum of f(x, y) = - 2y/(x^2 + y^2 + 1) on
the region R = {(x, y) such that x^2 + y^2 <= 4}
Express the answer as an ordered triple.

Find the complete solution to the following differential
equations.
a) y''+2y'-y=10
b) 2y''- y = 3x^2

Let f (x, y) = 100 sin(π(x−2y))/(1+x^2+y^2) . Find the
directional derivative of f 1+x^2+y^2 at the point (10, 6) in the
direction of: (a) u = 3 i − 2 j (b) v = −i + 4 j

f(x, y) = 4 + x^3 + y^3 − 3xy
(a,b)=(0.5,0.5)
u = ( √ 1 /2 , − √ 1 /2 )
a) Calculate the rate of change of f along the curve r(t) = (t,
t2 ), at t = −1
b)Classify the critical points of f using the second derivative
test.

x^2y''-3xy'+3y=x^-2

Let f(x, y) = 2x^3y^2 + 3xy^3 4x^3 y. Find
(a) fx
(c) fxx
(b) fy
(d) fyy
(e) fxy
(f) fyx

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 19 minutes ago

asked 31 minutes ago

asked 31 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago