Differential Equations Answers

In the Philippines, the COVID-19 cases drops from 386,000 in March, 2020 to 230,000 in July, 2020. If the cases is following an exponential pattern of decline, what is the expected cases in December, 2020?,

1. Solve the following Bernoulli's Differential Equations. Show your solutions.

a. dy/dx + (1/3) y = e^x y²

b. x (dy/dx) + y = xy³

c. dy/dx + (2/x) y = -x² cos x y²

d. x²y-x³ (dy/dx) = y² cos x

Find the equation of integral surface to the differential equation

2y(z-3)p+(2x-z)q=y(2x-3) which passes through the circle z=0 , (x)^2 + (y)^2 = 2x

(D^2 + 4) y = 4 sec 2x csc 2x

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.