How many solutions does a nth order differential equation have?

An nth order of differenential equation has a general solution which gives a family of curves. This is what I get after integrating the derivative and the addition arbitrary constant gives a family of curves. A family of curves is basically a function or an equation in x & y which has 1 or more arbitrary constant.

How many solutions can a differential equation have?

This question is usually called the existence question in a differential equations course. If a differential equation does have a solution how many solutions are there? As we will see eventually, it is possible for a differential equation to have more than one solution.

Why does an nth order differential equation have n solutions?

One can show that, for an nth order homogeneous differential equation, this vector space has dimension n. That is, there exist n independent solutions such that any solution can be written in terms of those n solutions.

Do all odes have a solution?

A first-order ODE (or PDE) with analytic coefficients always has a solution (which may or may not be expressible elementarily), by the Cauchy-Kowalewski Theorem . So in this sense, yes, it is possible to determine that they do, and the answer is always “yes”.

How many solutions can a first-order differential equation have?

one solution
Solutions, Slope Fields, and Picard’s Theorem Finally we present Picard’s Theorem, which gives conditions under which first-order differential equations have exactly one solution.

How many solutions are there for a first order ODE?

Solutions, Slope Fields, and Picard’s Theorem Finally we present Picard’s Theorem, which gives conditions under which first-order differential equations have exactly one solution.

What is nth order differential equation?

A general solution of an nth-order equation is a solution containing n arbitrary independent constants of integration. A particular solution is derived from the general solution by setting the constants to particular values, often chosen to fulfill set ‘initial conditions or boundary conditions’.