Differential Equations Answers

please solve this problem

L^-1 { (1/s^2) e ^(-y*sqrt(s+a)) } .

If x=3t☻-1,y=t♥-t,then dy/dx is equal to

1.If f(X)=4-2x/2+3x+3xpower2 then the values of x for which f'(X)=0 is
2.If y=(x+square root of x power 2 -1)power m then(x power 2 -1)(dy/dx)power 2-mpower2 y power2 is proved to be

pls solve inerse laplace problem :

L^-1{ a/(s+b)*exp(-y *sqrt(s+c))} .

A tank contains 20kg of salt dissolved in 5000L of water. Brine that contains 0.03kg of salt per litre of water enters the tank at a rate of 25L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt remains in the tank after half an hour?
(Hint: Let y(t) be the mass of salt at time t, then dy/dt = (rate in) - (rate out) is separable)

Solve the initial value problems:
a) y' = (x y sin(x))/(y+1), y(0) = 1
b) t(du/dt) = t^2 + 3u, t>0, u(2)=4

The number of bacteria doubles after every hour. If there were 30 bacteria originally find the number of bacteria after 3 days.

Solve with the orthogonal trajectory:
x y = c

solve xp+3yp=2(z-x2q2).

Solve the following by Banoulli equation?

dy/dx + xy/(1-x^2) = x y^1/2