Question

y"=2y' reducing this into y

Answer 1

Given the equation y"=2y'

Rewrite the equation to have

y"-2y'+0y=0

Where

p=-2

q=0

First of all,we should find the roots of the characteristics equation

$q+(k^2+kp)=0$

$0+(k^2-2k)=0$

$\implies k(k-2)=0$

$\therefore k_1=0$

$k_2=2$

The general solution is of the form

$y=C_1e^{k_1x}+C_2e^{k_2x}$

$y=C_1e^{0x}+C_2e^{2x}$

$\therefore y=C_1+C_2e^{2x}$