21MAT206 DIFFERENTIAL EQUATIONS MATHEMATICS PAPER – III-

Unit I-

Review of differential equations (order, degree, linear, nonlinear, implicit and explicit form of solution, general solutions, particular solution, singular solution), Exactness, non-exact equations reduce to exact form.

Equations of first order but of higher degree: Equations solvable for 𝑑_𝑦/𝑑_𝑥, y, x, equations in Clairaut’s form, equations reducible to Clairaut’s form.

Unit II-

Equations of Second order: Linear homogeneous differential equations with constant coefficients, Euler-Cauchy equation, Linear Non homogeneous Differential Equations: Wronskian, linear independence, Method of undetermined coefficients, Method of variation of parameters.

Unit III-

Systems of first order linear equations: Conversion of nth order differential equation to n first order differential equations, homogeneous linear system with constant coefficients, fundamental matrices, complex eigenvalues, repeated eigenvalues, simultaneous linear differential equations with constant coefficients, simultaneous linear differential equations with variable coefficients.

Unit IV-

Solutions of partial differential equations: 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 𝑝 = 𝜕𝜕𝑧/𝜕𝜕𝑥 and 𝑞 = 𝜕𝜕𝑧/𝜕𝜕y-

Unit V-

Classification of partial differential equations of second order, Homogeneous linear partial differential equations with constant coefficient of higher order, Nonhomogeneous linear partial differential equations of higher order.