Verifying Solutions to Differential Equations?

Question

show that t^2 + y^2 = C^2 defines solutions of the differential equation

t + yy' = 0

And how do you find the interval of existance?

thanks in advance =]

Answer 1

This DE is separable into dy and dt.

you have:

t+y (dy/dt) = 0

separate the y and t as well as the dy and the dt.

integrate both side (remember to combine the constants so you only need one constant instead of two)

then you'll see that the resulting equation is the same as the one you're trying to define.

good luck