ED Lab 9

https://rextester.com/l/octave_online_compiler

1)
y''' - 2 * y'' - 5 * y'

Rezolvare:
1)

pkg load symbolic
syms y(x)
dsolve(diff(y(x),3) - 2 * diff(y(x), 2) - 5*diff(y(x),x) + 6*y == exp(x) + x^2)
syms r A0 A2 A1 y1(x) y2(x) y3(x) yp(x)
solve(r^3 - 2*r^2 - 5*r + 6 == 0, r)

% y''' - 2y'' - 5y' + 6y = e^x
%yp(x) = A0 * x * exp(x)
%y1(x) = diff(yp(x), x)
%y2(x) = diff(yp(x), 2)
%y3(x) = diff(yp(x), 3)

%y3(x) - 2 * y2(x) - 5 * y1(x) + 6 * yp(x)
%ec1 = simplify(y3(x) - 2 * y2(x) - 5 * y1(x) + 6 * yp(x))

% y''' - 2y'' - 5y' + 6y = x^2

yp(x) = A2 * x^2 + A1*x + A0
y1(x) = diff(yp(x), x)
y2(x) = diff(yp(x), 2)
y3(x) = diff(yp(x), 3)

simplify(-4 * A2 - 5*(2*A2*x+A1) + 6*(A2*x^2 + A1*x +A0) == x^2)
%mai era ceva cred

2)

%syms y1(x) y2(x)
%y1(x) = diff(y(x), x)
%y2(x) = diff(y(x), 2)
%dsolve(diff(y(x), 3) - 2* diff(y(x), 2) + 5 * diff(y(x), x) == - 24 * exp(3 * x), y(0) == 4, y1(0) == -1, y2(0) == -5)

%dsolve(diff(y(x), 3) - 3 * diff(y(x), 2) + 3 * diff(y(x), x) - y - exp(x) - sin(x))