Answer to Question #96322 in Differential Equations for Olajide Olaitan

Question

If (y=2x+ce^x) is a solution of the differential equation frac {dy}{dx}-y=2(1-x) then find the particular solution satisfied by x=0, y=3

Answer 1

Q96322

Solution:

Given: $y= 2x + ce^x$ is general solution of the given differential equation.

To find: A particular solution of the given differential equation, when $x=0$, $y=3$

A general solution to a differential equation satisfies all particular cases,

thus, substituting the values of x, y in the general solution we get:

$y= 2x + ce^x,$

$3=2*0+ce^0,$

$3=0+c$

$\therefore c=3$ (for this particular case)

Thus, the particular solution satisfied by $x=0$, $y=3$ for the given differential equation is ;

$y=2x+3e^x$ (Answer)