Solve the differential equation x'' - x' - 2x = e^tcost -t^2 + cos^3(t)

Find the derivative of y = integral from x^2 to x^3 sin(t^3) dt using the fundamental theorem of calculus

Find the derivative of dy:dx = sqrt(1-2y^3)

Find the cross product of a and b using a_1 a_2 a_3 ...

Find the centroid of the region bounded by the given curves sinx and cosx

Find the centroid of the region bounded by the given curves sinx and cosx o and pi:4

Find the center of mass between the two functions x^2 and y^2

Find the arclength y = ln(1 - x^2), 0

The linear transformation T1:R2\toR2 is given by T(x,y)=(2x+3y,8x+13y)

The input is a constant multiple of an exponentila e^(at0. Suppose that there is a particular solution of the fomr Ae^at for some constant A. Find the constant A and determine the particular and general solution.

The half-life of plutonium is approximately 13 years. How much of a sample wieghing 8 g will remain after 110 years?

The differential equation is nonlinear in the form dx:dt=f(t,x), but linear (after some algebraic manipulations) if written as dt:dx=1:f(t,x). Find the general solution of the differential equation.

The current I(t) in an RLC circuit with voltage source E(t) is governed by thinitial value problem

The cone z=sqrt(x^2+y^2) and the plane z=1+y fin a vector function that represnets the curve intersection of the two surfaces

The closed interval [a,b] is a partitioned into n subintervals each of width Delta x = b-a:n if u is any number in the ith subinterval, what is lim

The amount of carbon 14 present after t years is given by the exponential equations. A sample from a refuse doposit

Evaluate the integral e^sqrt(x)

Evaluate the integral cos^3(x)sin(2x) dx from 0 to pi:2

Evaluate the integral (1 - tan(theta)):(1 + tan(theta)) dtheta

Evaluate the indefinite integral x:(x+2)^(2:3) hint let u = x+2

Evaluate the improper integral, or state that it diverges x:sqrt(1-x) from 0 to 1

Evaluate the improper integral from pi:4 to pi:2 tan (x) dx

Evaluate the improper integral, or state that it diverges

Evaluate the improper integral, or state that it diverges dx:(x^2+4)

Evaluate the improper integral, or state that it diverges dx:xln(x)

Evaluate the improper integral, or state that it diverges tan x from pi:4 to pi: 2