Answer to Question #172770 in Differential Equations for Yudhvir singh

Question

v) 2e^(x) is a particular integral for y'-y=2e^(x) . True or false

Answer 1

Solution.

$$y'-y=2e^x.$$

Сompose and solve the characteristic equation:

$\lambda-1=0, \newline \lambda=1.$

Therefore, $y=Ce^{\lambda x}=Ce^x,$ where $C$ is some constant, is the general solution of the equation.

If $C=2,$ then $y=2e^x$ is a particular integral, a solution of the equation.

Answer. Yes.