Differential Equations Answers

Solve the Partial differential equation

x² d²z/dx² - y² d²z/dy² + x dz/dx - y dz/dy = ln(x)

Solve the following boundary value problem.

uₙ = uₓₓ , 0 < x < L , n > 0

u(0,n) = u(L,n) = 0

u(x,0) = x(L-x) , 0 ≤ x ≤ L

Eliminate the arbitrary constant a from 2z=(ax+y)^2

Solve the differential equation

(z+z³) cosx dx - (z+z³) dy + (1-z²) (y-sinx) dz = 0

Solve the differential equation

(yz+z²) dx - xz dy + xy dz = 0

Find the general solution of the differential equation

y²/2 + 2y exp(t) + (y+exp(t)) dy/dt = 0

Solve the differential equation.

dx/ y²(x-y) = dy/ x²(x-y) = dz/ z(x²+y²)

Find the deflection of the fixed end vibrating string of unit length corresponding to zero initial deflection and u(x) given below as the initial velocity.

x , 0 ≤ x < 1/2
u(x) =
1-x , 1/2 ≤ x <1

Find the deflection of the fixed end vibrating string of unit length corresponding to zero initial deflection and u(x) given below as the initial velocity.

x , 0 ≤ x < 1/2
u(x) =
1-x , 1/2 ≤ x < 1

Solve the following boundary value problem .
uₙ = uₓₓ , 0<x<1 , n > 0
u(0,n) = u(l, n) = 0
u(x,0) = x (l - x) , 0 ≤ x ≤1