Differential Equations Answers

For 0 < x < 5 and t > 0 , solve the one-dimensional heat flow equation ∂u/ ∂t=4d^2u/dx^2 the conditions u (t, 0)= u( t ,5)= 0 ,u(0,x) = x .

a small bead can slide on a smooth wire AB being acted upon by force per unit mass equal to u÷ the square of its distance from a point O outside AB.find the oscillation.wher b is perpendicular distance from o toAB.

Solve: z( p − q )= z^2 +( x + y ^2)

Solve the following differential equations
i) y sin 2x dx =(1+ y² + cos² x) dy

ii) (xy² - x²) dx + ( 3x²y² + x²y - 2x³ + y²) dy =0

a small bead can slide on a smooth wire AB being acted upon by force per unit mass equalto u÷ the square of its distance from a point O outside AB.find the oscillation.wher b is perpendicular distance from O toAB.

Solve the differential equation y"=1+(y')^2

Find the deflection of vibration of string of unit length having fixed ends with initial velocity zero and initial deflection f(x)=a (x-x2)

. Find the general solution of the partial differential equation

6uxx −5uxy −6uyy =52e3x+2y

Dy/dx+{x/(1-x^2)}y=x√y,y(0)=1

Solve the following initial value problem

d^2 y/dx^2 + dy/dx -2y = -6 sin2x - 18 cos2x
y(0)=2 , y'(0)=2