Solve the equations $$\dfrac{dy}{dx}+ 2y = e^{3x}$$

Asked by Sakshi | 1 year ago |  72

##### Solution :-

From the question it is given that,

($$\dfrac{dy}{dx}$$) + 2y = e3x … [equation (i)]

The given linear differential equation is comparing with, ($$\dfrac{dy}{dx}$$) + py = Q

So, p = 2, Q = e3x

IF = e∫pdx

= e∫2dx

= e2x

Then, multiplying both side of equation (i) by IF,

e2x($$\dfrac{dy}{dx}$$) + e2x 2y = e2x × e3x

e2x($$\dfrac{dy}{dx}$$) + e2x 2y = e5x … [because am × an = am + n]

Now, integrating the above equation with respect to x,

ye2x = ∫e5x dx + c

ye2x = $$\dfrac{e^{5x}}{5}+c$$

y = ($$\dfrac{e^{5x}}{5}$$) + ce-2x

Answered by Aaryan | 1 year ago

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