## Quick Reference

A first-order differential equation *dy*/*dx*=*f*(*x*, *y*) in which the function *f*, of two variables, has the property that *f*(*kx*, *ky*)=*f*(*x*, *y*) for all *k*. Examples of such functions areAny such function *f* can be written as a function of one variable *v*, where *v*=*y*/*x*. The method of solving homogeneous first-order differential equations is therefore to let *y*=*vx* so that *dy*/*dx*=*xdv*/*dx*+*v*. The differential equation for *v* as a function of *x* that is obtained is always separable.

**From:**
homogeneous first-order differential equation
in
The Concise Oxford Dictionary of Mathematics »

*Subjects:*
Mathematics.

## Related content in Oxford Index

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.