Differential Equations Answers

Let an electrical circuit be governed by the following system of differential equation where i1,i2,i3 are the current in each branch of electrical circuit.find the current i1,i2,i3 internship branch of the electrical circuit by using diagonalisationmethod i1'=2i1+2i2+i3;i2'=i1+3i2+i3; i3'=i1+2i2+2i3

xydy/dx+4x²+y²=0 where y(2)=-7,x>0

Find the differential equation to the following;

dy/dx=9.8-0.196y

The continuous signal f(t) = cos(πt/2) sampled at 1 second intervals starting from t = 0.

(a) Find the Laplace transform of the sampled signal f*(t)

Solve the following IVP

y"-10y'+9y=5t;y(0)=-1,y'(0)=2

Exercise 5.

Find the solution of

dy/dx= e2x+y 2x+y

that has y = 0 when x = 0

The population in a town satisfies the logistic law.

dx/dt=x/100-x²/10⁸

where t is the number of years after the 2019 population census. if the population x was 100,000 in 2019.determine

1. population x as a function of time
2. The year the population will be double

solve the following differential equation

1. dx+(1-x²)dy=0
2. 8cos²ydx+cosec²xdy=0

The annual sells of a new company are expected to grow at a rate proportional to the difference between the sells and the upper limit of 20 million pounds . If the sells are 0 initially and 4million pounds after the 2^nd year of operations. Determine if the companies sells during the 10^th year and the year when the company sells will be 15million pounds.

solve each of the following initial value problems

1. (2x-5y)dx+(4x-y)dy=0 y(1)=4
2. (3x²+9xy+5y²)dx-(6x²+4xy)dy=0 y(1)=4

solve the following homogeneous equations

1. dy/dx=(2x-7y)/(3y-8x)
2. (2xy+3y²)dx-(2xy+x²)dy=0
3. xsin(y/x)(ydx+xdy)+ycos(y/x)(xdy-ydx)=0