What is the particular solution to the differential equation?

What is the particular solution to the differential equation?

A solution yp(x) of a differential equation that contains no arbitrary constants is called a particular solution to the equation.

How do you find the specific solution of a first order differential equation?

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.

Which of the following is a second order differential equation?

y′=y2.

How do you find the first order of a particular solution?

Here is a step-by-step method for solving them:

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.

What is the general solution to a differential equation?

The general solution is simply that solution which you achieve by solving a differential equation in the absence of any initial conditions. The last clause is critical: it is precisely because of the lack of initial conditions that only a general solution can be computed.

What does it mean to solve a differential equation?

A differential equation is a mathematical equation that involves variables like x or y, as well as the rate at which those variables change. Differential equations are special because the solution of a differential equation is itself a function instead of a number.

How to solve a differential equation?

– Put the differential equation in the correct initial form, (1) (1). – Find the integrating factor, μ(t) μ ( t), using (10) (10). – Multiply everything in the differential equation by μ(t) μ ( t) and verify that the left side becomes the product rule (μ(t)y(t))′ ( μ ( t) y ( t)) ′ – Integrate both sides, make sure you properly deal with the constant of integration. – Solve for the solution y(t) y ( t).

How can I solve this differential equation?

Solving.