Question

$\frac{d^{2}y}{d{x}^2}+(x^2+4x)\frac{dy}{dx}+y=x^8-8$

The above equation is a

• A. partial differential equation
• B. nonlinear differential equation
• C. non-homogeneous differential equation
• D. ordinary differential equation

Answer 1

Answer: (C), (D)

ordinary differential equation

$\frac{d^{2}y}{d{x}^2}+(x^2+4x)\frac{dy}{dx}+y=x^8-8$

A homogeneous equation is of the form

$\frac{dy}{dx}=\frac{f(x,y)}{g(x,y)}$

where, f(x,y) and g(x,y) are homogenous functions of the same degree in x and y. An ordinary differntial equation is that in which all differential coefficients are with respects to a single independent variable. A partial differential equation has two or more independent variable.

A differential equation is said to be linear if the independent variable and its differential coefficient occur only in first degree and not multiplied together.