Exercise
$\frac{dy}{dx}=y^2+2xy+x^2$
Step-by-step Solution
Learn how to solve separable differential equations problems step by step online. Solve the differential equation dy/dx=y^2+2xyx^2. The trinomial y^2+2xy+x^2 is a perfect square trinomial, because it's discriminant is equal to zero. Using the perfect square trinomial formula. Factoring the perfect square trinomial. 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\right) has the form Ax+By+C. Let's define a new variable u and set it equal to the expression.
Solve the differential equation dy/dx=y^2+2xyx^2
Final answer to the exercise
$y=\tan\left(x+C_0\right)-x$