Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Scegliere un'opzione
- Equazione differenziale esatta
- Equazione differenziale lineare
- Equazione differenziale separabile
- Equazione differenziale omogenea
- Prodotto di binomi con termine comune
- Metodo FOIL
- Load more...
We can identify that the differential equation $\left(x^2-y^2\right)dx+xy\cdot dy=0$ is homogeneous, since it is written in the standard form $M(x,y)dx+N(x,y)dy=0$, where $M(x,y)$ and $N(x,y)$ are the partial derivatives of a two-variable function $f(x,y)$ and both are homogeneous functions of the same degree
Learn how to solve problems step by step online.
$\left(x^2-y^2\right)dx+xy\cdot dy=0$
Learn how to solve problems step by step online. (x^2-y^2)dx+xydy=0. We can identify that the differential equation \left(x^2-y^2\right)dx+xy\cdot dy=0 is homogeneous, since it is written in the standard form M(x,y)dx+N(x,y)dy=0, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree. Use the substitution: y=ux. Expand and simplify. Apply the formula: b\cdot dy=a\cdot dx\to \int bdy=\int adx, where a=\frac{1}{-x}, b=u, dy=du, dyb=dxa=u\cdot du=\frac{1}{-x}dx, dyb=u\cdot du and dxa=\frac{1}{-x}dx.
