Exercise
$\frac{dy}{dx}=1+\left(\frac{1}{\left(x-y\right)^2}\right)$
Step-by-step Solution
Learn how to solve limits to infinity problems step by step online. Solve the differential equation dy/dx=1+1/((x-y)^2). 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 \left(x-y\right) 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 \left(x-y\right) 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=1+1/((x-y)^2)
Final answer to the exercise
$y+\arctan\left(x-y\right)=x+C_0+x$