AboutDr. Nyayapati Swami Expertise I can help you in solving first and second order differential equations. Questions must be at the Undergraduate level. Do not expect me to do all your homework.. If you have a homework question with no clues on how to go about, I will only give you some pointers on solving them.
Experience Ph.D. in Mathematics with more than 15 years of teaching. In addition to undergraduate calculus, I taught many more advanced subjects like Complex Analysis, General Topology, Numerical Analysis, Operations Research, Graph Theory, Mathematical Analysis, Mathematical Economics, Optimisation Theory.
Education/Credentials Ph.D. (University of Toledo, USA)
In the diagram the tangent to a curve at a general point p with coordinates (x,y) meets the x-axis at T.The point N on the x-axis is such that the PN is perpendicular to the x-axis.The curve is such that,for all values of x in the interval 0<x<(1/2)pi,the area of triangle PTN is equal to tan x,where x is in radians.Using the fact that the gradient of the curve at P is PN/(TN), show that dy/(dx)=1/2(y^2)cot x. ii) given that y=2 when x=1/6(pi),solve this differential equation to find the equation of the curve,expressing y in terms of x. I dont know how to do both the questions, can you please help me? Many thanks
Answer PN = y
PN/TN = dy/dx
y/TN = dy/dx
TN = y / (dy/dx)
)