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Divide both sides by dx and ($1+e^x$) to isolate $dy/dx$, yielding $dy/dx$ = (ye^x)/($1+e^x$). Then, move the term containing y to the left side to match the standard linear structure y' + $p(x)y = q(x)$.

Conditions: The equation is a first-order differential equation.; ($1+e^x$) is never zero, so division is valid.

Divide both sides by dx and ($1+e^x$) to isolate $dy/dx$, yielding $dy/dx$ = (ye^x)/($1+e^x$). Then, move the term containing y to the left side to match the standard linear structure y' + $p(x)y = q(x)$.

Conditions: The equation is a first-order differential equation.; ($1+e^x$) is never zero, so division is valid.

Take the reciprocal of both sides to swap the roles of the independent and dependent variables, yielding $dx/dy = (x+y^2)/y$. Split the fraction on the right side to get $dx/dy = (1/y)x + y$.

Conditions: The equation is a first-order differential equation.; y is not equal to zero, allowing division by y and taking the reciprocal.

Take the reciprocal of both sides to swap the roles of the independent and dependent variables, yielding $dx/dy = (x+y^2)/y$. Split the fraction on the right side to get $dx/dy = (1/y)x + y$.

Conditions: The equation is a first-order differential equation.; y is not equal to zero, allowing division by y and taking the reciprocal.

First, rearrange the terms to isolate the dy term: xdy = -(y - x sin x)dx. Divide both sides by dx and then by x to get $dy/dx = -(y - x \sin x)/x$.

Conditions: The equation is a first-order differential equation.; x is not equal to zero, allowing division by x.

First, rearrange the terms to isolate the dy term: xdy = -(y - x sin x)dx. Divide both sides by dx and then by x to get $dy/dx = -(y - x \sin x)/x$.

Conditions: The equation is a first-order differential equation.; x is not equal to zero, allowing division by x.