Verify that the implicit equation x^2 − y^2 = C, where C is a constant,represents a solution to the ODE y′ =x/y.

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

SOLVE THE ODE y''+9y=xexp(3x) + 6

Check by differentiation