Differential Equations Answers

A mass weighing 39.5 kg. streches a spring 1/4m. At t=0 , the mass is released from a point 3/4m below the equilibrium position with an upward velocity of (5/4)m/sec. Determine the function x(t) that describes the subsiquent free motion.

Solve : xy' - y =e to the power y'. Also obtain its singular solution.

A series RLC circuit with R-6 ohm, C-0.02 Farad and L=0.1 has no applied voltage . Find the subsiquent current in the circuit if the initial charge , on the capacitor is q and the initial current is zero.

According to Newton's law of cooling, the rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance and that of the air. If the temperature of the air is 290 degree centigrate and the substance cools from 370 to 330 degree centigrate in 10 minutes, find when the temperature will be 295 degee centigrate.

The set of real (or complex) situations of equation y'(x) +P(x) y(x) - Q(x) , forms a real (or complex) vector space.

the derivative of ln x - e^-3x and ln x - (x^2 - 4)

find the derivative of f(x) = ln x - e^3x and f(x) = ln x - ( x^2 - 4 )?

Solve the initial value problem:
(d^2x/dt^2)-3(dx/dt)-10x=0
x(0)=1 and x'(0)=0

Please solve the IVP for the unknown function u = u(x1,x2,x3):

x2(partial u with respect to x1) - x1(partial u with respect to x2) + (partial u with respect to x3) = x1

u(x1,x2,0) = x1^2 - x2.

Please solve the following Initial Value Problem pde:

xu_x + (1+y)u_y = x(1+y) + xu, u(-1,y) = *(y)

where *(y) is a given function such that *'(y) exists and is continuous. Explain why this condition on * must be satisfied.