Differential Equations Answers

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

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.

Show that 2z=(ax+y)^2+b,where a,b are arbitrary constants is a complete

integral of px+qy-q^2=0

a) Verify that the total differential equation

yz dx +(x^2y-zx)dy+(x^2z-xy)dz=0 is integrable and hence find its integral.