Differential Equations Answers

If a simple pendulum of length l oscillates through an angle α on either side of the mean position then find the angular velocity dt/dθ

of the pendulum where θ is the angle which the string makes with the vertical.

A particle of mass m is thrown vertically upward with velocity v0. The air resistance is mg cv^2 where c is a constant and v is the velocity at any time t. Show that the time taken by

the particle to reach the highest point is given by v0 underroot c= tan (gt underroot c )

: y^2 + x^2 (dy/dx)^2 -2xy (dy/dx) = 4 (dx/dy)^2

Solve : y^2 + x^2 (dy/dx)^2 -2xy (dy/dx) = 4 (dx/dy)^2

Solve the following ordinary differential equation.


=> d^2y/dx^2 + dy/dx + y = 0 .

Interpret the initial value problem d^2θ/dt^2+ß^2 θ=0, θ(0)=θ° ,dθ/dt] at (t=0) =ω°

for any physical situation and hence solve the problem

Solve the differential equation x^3 p^2 +x^2 yp+a^3=0 and also obtain its singular solution, if

it exists.

xdy/dx–y=e^(dy/dx)

d^2y/dx^2–cotxdy/dx–sinx^2 y=cosx–cos^3x

Find the integral surface of the partial differential equation:(x–y) y^2 p+(y–x)x^2 q=(x^2 +y^2)z through the curve xz=a^2, y=0