# 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.

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.

#### Practise This Question

If a=^i+2^j+2^k and b=3^i+6^j+2^k, then the vector in the direction of a and having magnitude as |b|, is