Differential Equations

An ordinary differential equation is given below. $x^2 \frac{d^2y}{dx^2} = 6y$ Considering $a$ and $b$ as arbitrary constants, the general solution of the equation is

Consider two Ordinary Differential Equations (ODEs): P: $\frac{dy}{dx} = \frac{x^4+3x^2y^2+2y^4}{x^3y}$ Q: $\frac{dy}{dx} = \frac{-y^2}{x^2}$ Which one of the following options is CORRECT?

The solution of the differential equation $\frac{d^3y}{dx^3} - 5.5 \frac{d^2y}{dx^2} + 9.5 \frac{dy}{dx} - 5 y = 0$ is expressed as $y = C_1e^{2.5 x} + C_2e^{\alpha x} + C_3e^{\beta x}$, where $C_1, C_2, C_3, \alpha$, an...

The solution of the second-order differential equation $\frac{d^2y}{dx^2} + 2\frac{dy}{dx} + y = 0$ with boundary conditions $y(0) = 1$ and $y(1) = 3$ is

If k is a constant, the general solution of dy/dx - y/x = 1 will be in the form of

For the Ordinary Differential Equation $\frac{d^2x}{dt^2} - 5\frac{dx}{dt} + 6x = 0$, with initial conditions $x(0) = 0$ and $\frac{dx}{dt}(0) = 10$, the solution is

The solution of the equation $x \frac{dy}{dx} + y = 0$ passing through the point (1,1) is

The solution of the equation $\frac{dQ}{dt} + Q = 1$ with $Q = 0$ at $t = 0$ is