Determine whether the given differential equation is

Question

Question # 1. Determine whether the given differential equation is separable or not?

dy/dx = 4y² - 3y + 1

Question # 2. x.dy/dx=1/y³

Rewrite in the form of a first order

Question # 3. x².dx+2ydy = 0, y(0) = 2

Question # 4. Newton's Law of Cooling. According to Newton Law of Cooling, if an object at temperature T is true M, then the rate of change of T is proportional to the difference of temperature M - T. This gives the differential equation: -

dT/dt=k(M-T)

a) Solve the differential equation for T

b) A Thermometer reading 100? is placed in a medicum having a constant temperature of 70? after six min, The thermometer reads 80?. What is the reading after 20 min?

Question # 5. Determine whether the given equation is separable, linear, neither, or both

(t² + 1) dy/dt = yt - y

Question # 6. In given problem obtain the general solution to the equation

dy/dx-y-e^3x = 0

Question # 7. Solve the initial value problem to the given equation: -

dy/dx + 4y-e^-x = 0, y(0) = 3/4

Question # 8. In example 2 the decay constant for the isotope RA1was 10/sec, which expresses itself in the exponent of the rate term 50e^-10tkg/sec. When the decay constant for RA₂ is k=2/sec, we see that in formula (14) for y the term (185/4) e^-2t eventually dominates (has greater magnitude for t large).

Redo example to taking k=20/sec. Now which term in the solution eventual dominates?

Redo example to taking k=10/sec.