Equations of First Order and of Degree Higher than one, Solvable for p, x, y and Clairaut’s Equation.

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 -Simultaneous Differential Equations with constant coefficients of the form i) f1(D)x + g1(D)y =Φ_1 (t) ii) f2(D)x + g2(D)y = Φ_2 (t) where f1 , g1 , f2 and g2 are rational functions D=d/dt with constant coefficients Φ_1and Φ_2 explicit functions of t.

Formation of equations by eliminating arbitrary constants and arbitrary 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 f(p, q) = 0, f(x, p, q) = 0 f(y, p, q) = 0 f(z, p, q) = 0, Claiarut’s form - Lagrange’s Linear Equations. .

Laplace Transforms: Definition – Laplace Transforms of standard functions –Linearity property – First Shifting Theorem – Transform of t f (t), f(t)/t, f 1(t), f 11(t).

Applications to solutions of First Order and Second Order Differential Equations with constant coefficients.