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# Differential Equations

Select from the following:
Differential equations. Definitions. Order,
degree. General, particular and singular solutions.

Differential equations of the first order and
first degree. Methods of solution. Separation of variables.
Homogeneous, exact and linear equations. Integrating factors.
Bernoulli's equation.

Equations of the first order and higher
degree, Clairaut's equation. Singular solutions and
extraneous loci. Discriminant of a differential equation.
p-discriminant, c-discriminant.

Second order differential equations

General solution of n-th order linear
differential equations. Linearly dependent and independent
sets of functions, Wronskian test for dependence.

Differential operators

Homogeneous linear differential equations
with constant coefficients, Auxiliary equation, solutions

Methods for finding particular solutions of
linear differential equations with constant coefficients.
Method of Undetermined Coefficients, Variation of Parameters,
Superposition. Operational methods.

Solutions to systems of simultaneous linear
differential equations with constant coefficients

Solution of linear differential equations by
power series. Solutions about ordinary points and singular
points.

Special functions. Bessel's equation of order
v. Bessel function of the first kind.

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