Exercise
$\frac{dy}{dx}=\left(y-x+3\right)^2$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(y-x+3)^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(y-x+3\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(y-x+3\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=(y-x+3)^2
Final answer to the exercise
$\frac{1}{\sqrt{3}}\arctan\left(\frac{y-x+3}{\sqrt{3}}\right)=x+C_0$