Differential Equations For Class 12

A differential equation is of the form \(\frac{dy}{dx} = g(x)\), where \(y = f(x)\).

Order of differential equation-

The highest order of the derivative present in the dependent variable with respect to the independent variable in the given differential equation.

\(\left ( \frac{d^{3}y}{dx^{2}} \right ) + x\left ( \frac{dy}{dx} \right )^{4} = 0\)

In the example given above, the order of the differential equation is 3.

Differential Equations For Class 12

General and Particular Solution of a Differential Equation-

The solution which contains arbitrary constants is called the general solution of the differential equation.

Whereas the solution free from arbitrary constants obtained from the general solution by giving particular values to the arbitrary constants is called a particular solution of the differential equation.

Differential Equations For Class 12
Differential Equations For Class 12


Practise This Question

If there are 45 birds out of 150 in a zoo which are migratory. 35 of the total birds are of  Indian origin. Which kind of birds are more in number in the zoo?