Question

Find the differential equation of $y=a{e}^{3x}+b{e}^{3x}$

Answer 1

To find Differential equation of the solution

$y=a{e}^{3x}+b{e}^{3x}$

$y=(a+b)e^{3x}$

let $a+b=c$ (some, constant)$

$y=c{e}^{3x}$

$y^1\left(x\right)=3c{e}^{3x}$ {No. of parometer in the gen soln imblies the order of the diffential earn}

$y^1\left(x\right)=3y\left(x\right)$

$y^1\left(x\right)-3y\left(x\right)=0$

$y^1-3y=0$