Final answer to the problem
$y=-2\arctan\left(\frac{x+C_1}{x+C_0}\right)+x+1$
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Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=sin(x-y+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 x-y+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 x-y+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.
Final answer to the problem
$y=-2\arctan\left(\frac{x+C_1}{x+C_0}\right)+x+1$
