Hello, I'm a little stuck on this problem:
Find a solution to the differential equation subject to the initial conditions.
Here is how I tried to solve the problem:
dt = tez , through the origin.
dt = tez
multiply both sides by dt, and then divide both sides by ez to get like variables with like variables:
ez = tdt Take the integral of both sides:
(integral sign) 1/ez
dz = (integral sign) t dt substitution
w = ez
dw = ez
(integral sign)1/w dz = (integral sign) t dt
ln|w| = t2
/2 + C
ln|ez| = t2/2 + C
exponentiate both sides to get rid of the natural log:
eln|ez| = et2/2 + C
the e and the natural log cancel out
ez = e(t^2)ec
ez = Ce(t^2) ----(where C is just a constant)
Now this is where I am stuck. Have I done it correctly so far? What do I need to do next? Please help. Thank you.