Step 1

There are four type of differential equations,

1. Ordinary Differential equation.

The ordinary differential equation consists of one or more functions of one independent variable along with their derivatives.

Example: \(\displaystyle{y}'={x}^{{2}}−{1}\).

2. Partial Differential equation.

The partial differential equation consists of partial derivatives of the dependent variable with more than one independent variable.

Example: \(\displaystyle\frac{{\partial^{{2}}{u}}}{{\partial{x}^{{2}}}}+\frac{{\partial^{{2}}{u}}}{{\partial{y}^{{2}}}}={0}\)

Step 2

3. Linear Differential equation.

The linear differential equation consists of derivatives of the dependent variable wit respect to one or more independent variable.

Example: \(\displaystyle\frac{{\partial{y}}}{{\partial{x}}}+{2}{y}={\sin{{x}}}\).

4. Homogeneous Differential equation.

The differential equation is of the form f(x,y)dy=g(x,y)dx. is said to be homogeneous differential equation.

Example : F(x,y)=22x−8y.

There are four type of differential equations,

1. Ordinary Differential equation.

The ordinary differential equation consists of one or more functions of one independent variable along with their derivatives.

Example: \(\displaystyle{y}'={x}^{{2}}−{1}\).

2. Partial Differential equation.

The partial differential equation consists of partial derivatives of the dependent variable with more than one independent variable.

Example: \(\displaystyle\frac{{\partial^{{2}}{u}}}{{\partial{x}^{{2}}}}+\frac{{\partial^{{2}}{u}}}{{\partial{y}^{{2}}}}={0}\)

Step 2

3. Linear Differential equation.

The linear differential equation consists of derivatives of the dependent variable wit respect to one or more independent variable.

Example: \(\displaystyle\frac{{\partial{y}}}{{\partial{x}}}+{2}{y}={\sin{{x}}}\).

4. Homogeneous Differential equation.

The differential equation is of the form f(x,y)dy=g(x,y)dx. is said to be homogeneous differential equation.

Example : F(x,y)=22x−8y.