Differential Equations Answers

Find the partial differential equation arising from f[z/x^3,y/z]=0, where f is an arbitrary function of the arguments. Also find the general solution of the PDE obtained.

Given that z = ax +sqrt (a^2 − 4y) + c is the complete integral of the PDE, p^2 − q^2 =4 determine its general integral.

Find the values of n for which the equation (n-1)²uxx - y^2n uyy = ny^(2n-1)uy is
i) parabolic ii) hyperbolic.

Find the differential equation of the family of surfaces φ[ z(x+y)² , x² ‐ y²] = 0

Find f(y) so that equation f(y)dx − zx dy − xy ln y dz = 0 is integrable. Also obtain the corresponding integral using Natani’s method.

Solve: z(p - q) = z² + (x + y²).

Solve the following equations:
(i) (D² + DD′ + D + D′ + 1)z = 0
(ii) (D² − 2DD′+ D′²)z = tan(y + x).

Find the integral curves of the equation:
dx/(x²+y²) = dy/2xy = dz/{z(x+y)}

A series RLC circuit withR = 6 ohm, C = 0.02 Farad and L = 0.1 has no applied voltage. Find the subsequent current in the circuit if the initial charge, on the capacitor is q0 and the initial current is zero.

Solve the following differential equations:
i) y sin2x dx = (1+ y²+ cos²x) dy
ii) (xy² - x²)dx + (3x²y² + x²y - 2x³ + y²)dy = 0