Review of differential equations (order, degree, linear, nonlinear, implicit and explicit form of solution, general solutions, particular solution, singular solution). Exactness, nonexact equations reduce to exact form.
Equations solvable for ����
Clairaut’s form.
����, y, x, equations in Clairaut’s form, equations reducible to
Linear homogeneous differential equations with constant coefficients, Euler Cauchy equation, Linear Nonhomogeneous Differential Equations: Wronskian, linear independence, Method of undetermined coefficients. Method of variation of parameters.
Conversion of nth order differential equation to n first order differential equations, homogeneous linear system with constant coefficients, fundamental matrices, complex eigen values, repeated eigenvalues. simultaneous linear differential equations with constant coefficients, simultaneous linear differential equations with variable coefficients.
Review of partial differential equations (order, degree, linear, nonlinear).
Formation of equations by eliminating arbitrary constants and arbitrary functions. General, particular and complete integrals. Lagrange’s linear equation, Charpit’s method, Methods to solve the first order partial differential equations of the forms f(p,q) = 0, f(z,p,q) = 0, f1(x,p) = f2(y,q) and Clairut’s form z = px + qy + f(p,q) where �� =����
���� and �� =����
����.
Homogeneous linear partial differential equations with constant coefficient of higher order. Non-homogeneous linear partial differential equations of higher order, method of separation of variables.
