# Are all exact equations separable?

## Are all exact equations separable?

A first-order differential equation is exact if it has a conserved quantity. For example, separable equations are always exact, since by definition they are of the form: M(y)y + N(t)=0, so ϕ(t, y) = A(y) + B(t) is a conserved quantity.

How do you know if an equation is exact?

Higher-order equations are also called exact if they are the result of differentiating a lower-order equation. For example, the second-order equation p(x)y″ + q(x)y′ + r(x)y = 0 is exact if there is a first-order expression p(x)y′ + s(x)y such that its derivative is the given equation.

### What is Bernoulli’s equation in maths?

A Bernoulli differential equation is an equation of the form y′+a(x)y=g(x)yν, where a(x) are g(x) are given functions, and the constant ν is assumed to be any real number other than 0 or 1. Bernoulli equations have no singular solutions.

Which is the solution to the EQ World equation?

[f(eαxym) + mxg(eαxym)]y′= y[h(eαxym) − αxg(eαxym)]. The EqWorld website presents extensive information on solutions to various classes of ordinary differential equations, partial differential equations, integral equations, functional equations, and other mathematical equations.

#### Where can I find the EQ World website?

The EqWorld website presents extensive information on ordinary differential equations , partial differential equations , integral equations , functional equations , and other mathematical equations. Website location: Institute for Problems in Mechanics, Russian Academy of Sciences, 101 Vernadsky Avenue, Bldg 1, 119526 Moscow, Russia.

What kind of Math is on EQ World?

EqWorld is a free online mathematics reference site that lists information about mathematical equations. It covers ordinary differential, partial differential, integral, functional, and other mathematical equations.