Find a second solution y2(x) of
x^2y"-3xy'+5y=0; y1=x^2cos(lnx)

We can try reduction order and look for a solution . Then

Substituting these into the ODE gives

which leaves us with an ODE linear in :

This ODE is separable; divide both sides by the coefficient of and separate the variables to get

Integrate both sides; on the right, substitute so that .

Now solve for ,

then for ,

Solve for by integrating both sides.

Substitute again and solve for :

then for ,

So the second solution would be

already accounts for the second term of the solution above, so we end up with

as the second independent solution.

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc