Suppose is another solution. Then
Substituting these derivatives into the ODE gives
Let , so that
Then the ODE becomes
and we can condense the left hand side as a derivative of a product,
Integrate both sides with respect to :
Solve for :
Solve for :
So another linearly independent solution is .
Answer:
1 seconds after being thrown, the stone reaches its max height
Step-by-step explanation:
The parabolic (quadratic) equation is:
Lets expand this in the form , so we have:
We can say the values of a,b, and c, now to be:
a = -5
b = 10
c = 40
The number of seconds at which the max would occur is given by the point, x, at:
We know a and b, let's find the seconds, x,
Hence,
1 seconds after being thrown, the stone reach its max height