Differential Equations - Engineering Mathematics - Agricultural Engineering Previous Year Questions

Solution of the ordinary differential equation \(\frac{dy}{dx} = \frac{x^2 + y^2}{y}\) is

Solution of the differential equation \(\frac{dy}{dx} - 7y = e^x\) is

A particular solution of \( \frac{d^2 y}{dx^2} + 5 \frac{dy}{dx} - 3y = 6 \) is

The partial differential equation \( \frac{\partial^2 u}{\partial x^2} - 7 \frac{\partial^2 u}{\partial x \partial y} + 2 \frac{\partial^2 u}{\partial y^2} = 0 \) is said to be

Identify the following partial differential equations in the given order based on their generic form where \(c\) is a constant, and \(u_1\) and \(u_2\) are functions of \((x, t)\) and \((x, y)\), respectively:
(i) \(\frac{\partial^2 u_1}{\partial t^2} = c^2 \frac{\partial^2 u_1}{\partial x^2}\)    (ii) \(\frac{\partial u_1}{\partial t} = c^2 \frac{\partial^2 u_1}{\partial x^2}\)    (iii) \(\frac{\partial^2 u_2}{\partial x^2} + \frac{\partial^2 u_2}{\partial y^2} = 0\)

The general solution to the ordinary differential equation \(\frac{d^2 y}{dx^2} = \cos 2x\) is