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Exercise 5.
Find the solution of
dy/dx= e2x+y 2x+y
that has y = 0 when x = 0
If money is deposited into an account at a continuous rate of 2000 shillings per year and the account earns 8% compounded continuously. Find the amount in the account at any time t and the amount in the account after 5years if initially the account had 10000 shillings.
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
- population x as a function of time
- The year the population will be double
solve the following differential equation
- dx+(1-x2)dy=0
- 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 2nd year of operations. Determine if the companies sells during the 10th year and the year when the company sells will be 15million pounds.
solve each of the following initial value problems
- (2x-5y)dx+(4x-y)dy=0 y(1)=4
- (3x2+9xy+5y2)dx-(6x2+4xy)dy=0 y(1)=4
solve the following homogeneous equations
- dy/dx=(2x-7y)/(3y-8x)
- (2xy+3y2)dx-(2xy+x2)dy=0
- xsin(y/x)(ydx+xdy)+ycos(y/x)(xdy-ydx)=0
Solve the initial-value problem: (dx/dt)+(tant)x=(cost)^2, x(0)=-1.
(2y^3-x^3)dx+3x^2ydy=0
