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.
How are ordinary differential equations solved in EqWorld?
EqWorld The World of Mathematical Equations Home PageExact SolutionsMethodsSoftwareEducationAbout This SiteMath Forums Exact Solutions> Ordinary Differential Equations> First-Order Ordinary Differential Equations PDF version of this page 1. First-Order Ordinary Differential Equations y′= f(y). Autonomous equation. y′= f(x)g(y).
