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Study BSc - Differential Equation

Unit I: Ordinary Differential Equations: Equations of First Order and of Degree Higher than one – Solvable for p, x, y – Clairaut’s Equation – Simultaneous Differential Equations with constant coefficients of the form i) f1(D)x + g1(D)y = ( ) 1 f t ii) f2(D)x + g2(D)y = ( ) 2 f t where f1 , g1 , f2 and g2 are rational functions dt d D = with constant coefficients 1 f and 2 f explicit functions of t. Unit II: Finding the solution of Second and Higher Order with constant coefficients with Right Hand Side is of the form Veax where V is a function of x – Euler’s Homogeneous Linear Differential Equations – Method of variation of parameters. Anx.18 D - B.Sc Maths (SDE) 2007-08 Page 6 of 26 Unit III: Partial Differential Equations: Formation of equations by eliminating arbitrary constants and arbitary functions – Solutions of P.D Equations – Solutions of Partial Differential Equations by direct integration – Methods to solve the first order P.D. Equations in the standard forms - Lagrange’s Linear Equations. Unit IV: Laplace Transforms: Definition – Laplace Transforms of standard functions – Linearity property – Firsting Shifting Theorem – Transform of tf(t), ( ) t f t , f1(t), f11(t). Unit V: Inverse Laplace Transforms – Applications to solutions of First Order and Second Order Differential Equations with constant coefficients.




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