Summary

Videos

References

Consider the differential equation dy/dx = e^{x} - 4

We claim that function y = e^{x} - 4x + 3 is the solution of the differential equation.

The solution of a differential equation is the function that satisfies it.

There exist two types of solutions for a differential equation:

1. General solution

2. Particular solution

dy/dx = e^{x} - 4

y = e^{x} - 4x + 3

Suppose function y is of the forms as shown.

y = e^{x} - 4x + 5 â‡’ dy/dx = e^{x} - 4

y = e^{x} - 4x - 5 â‡’ dy/dx = e^{x} - 4

y =e^{x} - 4x + 122 â‡’ dy/dx = e^{x} - 4

Each of the three forms of the function y entitles to be the solution of the differential equation, since their derivatives are the same.

y = e^{x} - 4x + C

We can represent the constant in the equations with a letter. We chose C here.

So, this function represents all the solutions of the differential equation. Such a function is called the general solution.

And, the function obtained by replacing the value of 'C' by a number is called the particular solution.

Consider the differential equation dy/dx = e^{x} - 4

We claim that function y = e^{x} - 4x + 3 is the solution of the differential equation.

The solution of a differential equation is the function that satisfies it.

There exist two types of solutions for a differential equation:

1. General solution

2. Particular solution

dy/dx = e^{x} - 4

y = e^{x} - 4x + 3

Suppose function y is of the forms as shown.

y = e^{x} - 4x + 5 â‡’ dy/dx = e^{x} - 4

y = e^{x} - 4x - 5 â‡’ dy/dx = e^{x} - 4

y =e^{x} - 4x + 122 â‡’ dy/dx = e^{x} - 4

Each of the three forms of the function y entitles to be the solution of the differential equation, since their derivatives are the same.

y = e^{x} - 4x + C

We can represent the constant in the equations with a letter. We chose C here.

So, this function represents all the solutions of the differential equation. Such a function is called the general solution.

And, the function obtained by replacing the value of 'C' by a number is called the particular solution.