# Differential equations

Please see the attached file.

dy/dx = 3/y

First find a general solution of the differential equation. Then find a particular solution that satisfies the initial condition y(0) = 5.

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A bacteria population is increasing according to the natural growth formula and numbers 100 at 12 noon and 156 at 1 p.m. Write a formula giving P(t) after t hours.

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Apply Euler's method to the initial value problem below so as to approximate its solution on the interval [0, ½].

dy/dx = -(y + x) ; y(0) = -1

Use step size h = 0.1.

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Find the particular solution of the differential equation

x(dy/dx) + 3y = 5x

subject to the initial condition y(1) = 1.

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The time rate of change of an alligator population P in a swamp is proportional to the square root of P. The swamp contained 9 alligators in 1990 and 25 alligators in 1995. When will there be 49 alligators in the swamp?

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Find the general solution of the differential equation: y'' + 2y' + 5y = 0.

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Solve the initial value problem: y'' + 6y' + 25y = 0; y(0) = 5, y'(0) = 1.

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The equation x'' + 16x = 28cos 3t; x(0) = x'(0) = 0, describes forced undamped motion of a mass on a spring. Express the position function x(t) as the sum of two oscillations.

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Given a = <-4, -4> and b = <-5, -6>,

find (a) |a|

(b) |-2b|

(c) |a - b|

(d) a + b,

(e) 3a - 2b

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A particle moves in space. Its position vector at time t is r(t) = ti + j sin t + k cos t. Find the velocity and acceleration vectors at time t = 0.

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#### Solution Summary

This is a series of problems with differential equations, including general solutions, initial value problems, Euler's method and particular solutions.