Learn how to solve problems step by step online. Solve the differential equation dy/dx=(y-x+1)/(y-x+-1). When we identify that a differential equation has an expression of the form Ax+By+C, we can apply a linear substitution in order to simplify it to a separable equation. We can identify that y-x+1 has the form Ax+By+C. Let's define a new variable u and set it equal to the expression. Isolate the dependent variable y. Differentiate both sides of the equation with respect to the independent variable x. Now, substitute y-x+1 and \frac{dy}{dx} on the original differential equation. We will see that it results in a separable equation that we can easily solve.

Solve the differential equation dy/dx=(y-x+1)/(y-x+-1)