Differential Equations Answers

Tank A initially contains 200 liters of brine containing 225 N of salt. Eight liters of fresh water per minute enter A and the mixture, assumed uniform, passes from A to B, initially containing 200 liters of fresh water, at 8 liters per minute. The resulting mixture, also kept uniform, leaves B at the rate of 8 liters per minute. Find the amount of salt in tank B after one hour.

Application of First Order of Differential Equation

Find two power series solutions of the given differential equation about the ordinary point x = 0. y'' - y = 0

(x^2D^2-xD+1)y=sin (logx)

An electromotive force 120, 0<t<20, E(t) = (o, t >20, is applied to an LR-series circuit in which the inductance is 20 henries and the resistance is 2 ohms. Find the current it) if i(0)-0.

Solve the following differential equation:

1. (D²+D)y=sin x

2. (D²+4D+5) y= 50x + 13e^3x

3. (D³+D²-4D-4)y= 4 sin x

4.(D³-D)y=x

5. (D²-4D+4)y=e^x

y''+2y'=0 find two power series of the given differential equation about ordinary point x=0.Compare the series of the solution with the solution of differential obtained using the method section 4.3.Try to explain any differences between the two forms of the solution.

A circuit has in series an electromotive force given by E=40-sin35tV, a resistor of 10Ω, and an inductor of 0.4H . If the initial current is 2 , find the current at time t>2.

0.4i'+10i=40-sin35t

Find the solution of Non-exact D.E

Given:

(x+4y^3)dy-ydx=0