Differential Equations Answers

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.

Solve the following Second Order equation with constant co-efficient

y’’ - 6y’+25 y = 0.

Solve the following second order non-homogenous equation:

y" + y = sin (2x)

Solve the following Bernoulli's initial value problem differential equation:

6y’ — 2y=xy⁴ y(0)=–2

Solve the following initial value problem equation:

2x²y" + 3xy' 15y = 0, y (1)=0 y' (1) = 1

Solve the differential equation:

a) yk - y(k-1) + 2y(k-2) = k² + 5k

b) y(k+2) - 4y(k+1) + yk = 3k +2^k

In LHS yk , y(k-1) and so on is not in multiply but the k part is written in down to y( like yk is not y×k but the k is written in right down of y).

A string of length l has it's ends x=0 and x=l fixed. It is released from its rest in position y=[4 lamda x(l-x)]/l². Find an expression of the displacement of the string at any subsequent time.

Find a general solution of (4D^2+4D+17)y= 0

(2x+y-4)dx+(x-3y+12)dy=0 solve using COEFFICIENT LINEAR IN TWO VARIABLES

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