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Differential Equations
Find the integral surface of the linear PDE
x(y²+z)p - y(x²+z)q = (x²-y²)z , which contains the straight line x+y =0 , z=1 .
x(y²+z)p - y(x²+z)q = (x²-y²)z , which contains the straight line x+y =0 , z=1 .
Differential Equations
Find the orthogonal trajectories of the family of parabolas x = cy²
Differential Equations
(D² + 3DD '+ 2D'²) z = x+y
Differential Equations
Solve the Partial differential equation
x² d²z/dx² - y² d²z/dy² + x dz/dx - y dz/dy = ln(x)
x² d²z/dx² - y² d²z/dy² + x dz/dx - y dz/dy = ln(x)
Differential Equations
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
uₙ = uₓₓ , 0 < x < L , n > 0
u(0,n) = u(L,n) = 0
u(x,0) = x(L-x) , 0 ≤ x ≤ L
Differential Equations
Eliminate the arbitrary constant a from 2z=(ax+y)^2
Differential Equations
Solve the differential equation
(z+z³) cosx dx - (z+z³) dy + (1-z²) (y-sinx) dz = 0
(z+z³) cosx dx - (z+z³) dy + (1-z²) (y-sinx) dz = 0
Differential Equations
Solve the differential equation
(yz+z²) dx - xz dy + xy dz = 0
(yz+z²) dx - xz dy + xy dz = 0
Differential Equations
Find the general solution of the differential equation
y²/2 + 2y exp(t) + (y+exp(t)) dy/dt = 0
y²/2 + 2y exp(t) + (y+exp(t)) dy/dt = 0
Differential Equations
Solve the differential equation.
dx/ y²(x-y) = dy/ x²(x-y) = dz/ z(x²+y²)
dx/ y²(x-y) = dy/ x²(x-y) = dz/ z(x²+y²)
