5. Solve the differential equation y" - 5y "+7y'-3y=0.​

The differential equation

y''' - 5y'' + 7y' - 3y = 0

has characteristic equation

r ³ - 5r ² + 7r - 3 = (r - 3) (r - 1)² = 0

with roots at r = 3 and r = 1 (with multiplicity 2), so that the characteristic solution to the DE is

y = C₁ exp(3x) + C₂ exp(x) + C₃ x exp(x)

Simplifying

42y = 8526

Solving

42y = 8526

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Divide each side by '42'.

y = 203

Simplifying

y = 203