Question

Find the general solution of the following differential equation :
dy/dx+ 2y = e^3x
​

Answer 1

Answer:

$y = \frac{ {e}^{3x} }{5} + c {e}^{ - 2x}$

Step-by-step explanation:

In this type of questions :

$\frac{dy}{dx} + py = q$

First we find ,

•IF

( Integrating factor) =

${e}^{ \int \: pdx}$

And ,At last :

•y(I•F)=

$\int \: (IF) \: qdx$

solution refer to the attachment

Answer 2

Step-by-step explanation:

dy/dx+2y=e^(3x)

P(x) = 2, Q(x) = e^(3x)

IF = e^[2∫dx] = e^(2x)

ye^(2x) = ∫ e^(3x) * e^(2x)dx

ye^(2x) = ∫ e^(5x)dx

ye^(2x) = 1/5e^(5x) + C

y = Ce^(-2x) + e^(3x)/5 answer//