Can an ode have no solution?

Absolutely! There are a ton of trivial examples. 2 and 3 have solutions for y as a function from the complex plane to itself, but not from the real line to itself.

Can all ODEs be solved?

It is not always possible to solve ordinary differential equations analytically. There are also some particular ODEs which can be solved by using suitable transformations. We will now outline each of these types of equation and the ways in which they can be solved.

How to solve first order differential equation?

Substitute y = uv,and dy dx = u dv dx+v du dx into dy dx+P (x)y = Q (x)

Factor the parts involving v

Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)

Solve using separation of variables to find u

Substitute u back into the equation we got at step 2

Solve that to find v

What makes an equation nonlinear?

A simple non-linear equation is of the form: ax2 + by2 = c. A non-linear equation look like a curve when graphed. It has a variable slope value. The degree of a non-linear equation is at least 2 or other higher integer values. With the increase in the degree of the equation, the curvature of the graph increases.

What are first order differential equations?

A first order differential equation is an equation involving the unknown function y, its derivative y’ and the variable x. We will only talk about explicit differential equations.

How do you solve one step equations?

Solve a two step equation by multiplying at the end instead of dividing. The principle for solving this type of equation is the same: use arithmetic to combine the constants, isolate the variable term, and then isolate the variable without the term. Let’s say you’re working with the equation x/5 + 7 = -3.