# What is the solution of the first order differential equation?

## What is the solution of the first order differential equation?

A first order differential equation is an equation of the form F(t,y,˙y)=0. A solution of a first order differential equation is a function f(t) that makes F(t,f(t),f′(t))=0 for every value of t. Here, F is a function of three variables which we label t, y, and ˙y.

**What is the first order equation?**

A first order differential equation is an equation of the form F(t,y,y′)=0. F ( t , y , y ′ ) = 0 .

**How do you solve LDE?**

Steps

- Substitute y = uv, and.
- 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 is general solution of differential equation?

A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)

**What is general solution and particular solution of differential equation?**

A solution yp(x) of a differential equation that contains no arbitrary constants is called a particular solution to the equation. GENERAL Solution TO A NONHOMOGENEOUS EQUATION. Let yp(x) be any particular solution to the nonhomogeneous linear differential equation. a2(x)y″+a1(x)y′+a0(x)y=r(x).

**How do you solve a first order differential equation?**

A first order differential equation is linear when it can be made to look like this: dy dx + P(x)y = Q(x) Where P(x) and Q(x) are functions of x. To solve it there is a special method: We invent two new functions of x, call them u and v, and say that y=uv. We then solve to find u, and then find v, and tidy up and we are done!

## What is an example of a first order differential equation?

A differential equation of order 1 is called first order, order 2 second order, etc. Example: The differential equation y” + xy’ – x 3y = sin x is second order since the highest derivative is y” or the second derivative.

**What is the general solution of differential equation?**

The solution of Differential Equations. The general solution of the differential equation is the relation between the variables x and y which is obtained after removing the derivatives (i.e., integration) where the relation contains arbitrary constant to denote the order of an equation.

**How do you solve this differential equation?**

Multiply everything in the differential equation by μ (t) and verify that the left side becomes the product rule (μ (t)y (t))′ and write it as such. Integrate both sides, make sure you properly deal with the constant of integration. Solve for the solution y (t). Let’s work a couple of examples.