Question

eliminate the arbitrary constant using any method

15.y\:=\:C_1e^{−3x}\:-2C_2e^{-3x}

Answer 1

$$y=C_1e^{-3x}-2C_2e^{-3x}$$

$$y=C_3e^{-3x}$$

Dividing throughout by $e^{-3x},$ we get

$$ye^{3x}=C_3$$

Differentiating with respect to $x,$ we get

$$e^{3x}y'+3e^{3x}y=0$$

Dividing throughout by $e^{3x},$ we get

$$y'+3y=0$$