# Find the general solution of the given differential equation. dy/dx + y = e^{7x}

**Solution:**

The given differential equation is

dy/dx + y = e^{7x}

It is of the linear differential equation form dy/dx + Py = Q

P = 1 and Q = e^{7x}

Let us find the integrating factor(IF)

I= e^{∫pdx} = e^{∫1. dx} = e^{x}

Now multiply the differential equation with IF

y × IF = ∫Q× IF .dx + C

Substituting the values

e^{x}.y = e^{x}(e^{7x}) + C

e^{x}.(y) = e^{8x} /8 + C

So we get

y = e^{8x} /8 e^{x} + c. e^{-x}

y = e^{7x}/8 + c.e^{-x}

Therefore, the general solution is y = e^{7x}/8 + c.e^{-x}.

## Find the general solution of the given differential equation. dy/dx + y = e^{7x}

**Summary:**

The general solution of the given differential equation dy/dx + y = e^{7x} is y = e^{7x}/8 + c.e^{-x}.

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