--Solve the initial value problem:

dy/dx= 2e^(y)/(1+x^2), y(0)=0.

--Express the solution of the given initial-value problem in terms of an integral-defined

function.

3dy/dx + (6 cosx)y=x, y(0) = 4dx

--Solve the initial value problem

y''4y'+4y=0, y(0)=3, y'(0)=5.

--A mass weighing 16 pounds stretches a spring 8 feet. Determine the equation of motionx(t) if the mass is initially released from equilibrium with an upward velocity of 6 ft/s^2. Remember that the acceleration due to gravity is 32ft/s^2 .

--Laplace inverse of {36/(s+2)^2(s4)}

-- y"+4y= (t (pi/2)). y(0)=0, y'(0)=1

-- Solve the given initial-value problem.

dx/dt=x+ 2y,

dy/dt=2x+y, subject tox(0) = 3 andy(0) = 5.