Exercise
$\frac{dy}{dx}=cos\left(y-x\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=cos(y-x). 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 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 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=cos(y-x)
Final answer to the exercise
$\ln\left(\sec\left(y-x\right)+\tan\left(y-x\right)\right)=x+C_0$