Answer to Question #301662 in Differential Equations for Nik

Question

Solution of differential equation p^ 2 +5p+6=0 is...

Answer 1

Solution

If p = du/dx solving given equation we will get $p_{1,2}=-2.5\pm\sqrt{{2.5}^2-6}=-2.5\pm0.5$

So given differential equation  may be rewritten in the form

(du/dx + 2)( du/dx + 3)=0

du₁/dx=-2 and du₂/dx = -3  => u₁ = -2x + C, u₂ = -3x + D

So given differential equation  has two solutions (C and D are arbitrary constants)

u₁(x) = -2x + C

u₂(x) = -3x + D