Consider the differential equation

Make a change of variable where is a function of and is a constant and solve the differential equation.

**Incomplete.**

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Stumbling Robot

A Fraction of a Dot
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Solve the differential equation *(1 + y*^{2}e^{2x}) y′ + y = 0

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### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Consider the differential equation

Make a change of variable where is a function of and is a constant and solve the differential equation.

**Incomplete.**

We have the equation

Which can be re-written as

Now, we use our substitution of variable

Giving us

Cancelling out the exponential on each side gives us

Now, a small change in notation to make the rest more intuitive. Using Leibniz notation instead of prime notation, as u and u’ are functions of x.

If we set m = -1, the equation becomes separable

Separating variables and integrating both sides gives us

Now, we can substitute u as follows

Simplifying terms gives us

Which is our back-of-book answer.