How do you solve first order linear differential equations?

Steps

1. Substitute y = uv, and.
2. Factor the parts involving v.
3. Put the v term equal to zero (this gives a differential equation in u and x which can be solved in the next step)
4. Solve using separation of variables to find u.
5. Substitute u back into the equation we got at step 2.
6. Solve that to find v.

How to learn differential equations in Khan Academy?

Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom.

How are the solutions of a linear differential equation found?

The solutions of a homogeneous linear differential equation form a vector space. In the ordinary case, this vector space has a finite dimension, equal to the order of the equation. All solutions of a linear differential equation are found by adding to a particular solution any solution of the associated homogeneous equation.

Can a non linear differential equation be homogenous?

In your example, since dy/dx = tan (xy) cannot be rewritten in that form, then it would be a non-linear differential equation (and thus also non-homogenous, as only linear differential equation can be homogenous). Comment on Yamanqui García Rosales’s post “The term “degree” can only be used to qualify poly…”

Is there a set method for solving differential equations?

Unfortunately, for most differential equations, is a mixture of practice and experience that gives you an idea of what kind of equation might be the solution. There is not a set method in order to find what family of function would make a good solution for a particular differential equation.