cahier physique - physics workbook

HOME in construction QUICK REVIEW OF COMPLEX NUMBERS
part1: first order linear differential equations
first order linear differential equations Y' + P(x) Y = q(x) (typo: the integrating factor is u= e^{(integral(p(x) dx)})
solution: (yu)' = q(x) u integrate both sides.

direct and inverse substitution Bernouilli equation y'=p(x) + q(x) yⁿ and y' = F (y/x)

sketching the solution of y' = f(y) bank account and embezzlement / logistic equations

review complex numbers, complexification of a linear first order differential equation y' + ky = k cos (wt)
(typo: modulus(z1z2) = r1r2 not r1 + r2)

more on y' + ky = k cos (wt), how to compute the real part by going catersian / 2 proofs for Acos g + B cos g = C cos (g - r )

solving y' + ky = k q(t) and yi + ky = q(t) / general solution / more examples (mixing problem, RC circuit)\

part2:second order linear differential equations

solving y'' + Ay' + By = 0 (homogeneous form) - 3 cases (2 real roots, 1 single real root, 2 complex roots)

2nd approach to write the solution of y'' +Ay' + By = 0 when the roots are complex

more on under damped solutions of y'' +Ay' + By = 0 , complex roots

Normalized solutions of y'' +Ay' + By = 0

introduction to inhomogeneous 2nd order linear equation y'' + Ay' + By = f(x)

link to solve first order linear DE