Differential Equations Answers

State and prove existence and uniqueness theorem

find the integral surface of the equation : (x-y)y^2p + (y- x)x^2q=(x^2 + y^2)z,
through the curve xz =a^2, y = 0

What is the degree and the order of this equation
y”y-(y’)^2=2

d^2y/dx^2 + 2dy/dx * d^3y/dx^3 +x=0

What is the degree and the order of y’-y^7=0

State and prove existence and uniqueness theorem.

(D^2-2DD'+D^2)z=12xy

Solve: e^(x)sinydx + (e^x +1)cosydy=0

(i) Use method of separation of variables in rectangular coordinates to obtain the following harmonic functions which are bounded in the upper half plane y > 0 of R2,
e−λy cosλx, e−λy sinλx; λ ≥0.
(ii) By integration with respect to the parameter λ, obtain the functions
x / x2 +y2, y / x2 +y2 which are harmonic in the upper half plane y > 0 of R2.