Differential Equations · Mathematics · NDA

Let $y_1(x)$ and $y_2(x)$ be two solutions of the differential equation $\frac{dy}{dx} = x$. If $y_1(0) = 0$ and $y_2(0) = 4$, then what is the number of points of intersection of the curves $y_1(x)$ and $y_2(x)$?

The differential equation, representing the curve $y = e^{x}(a\cos{x} + b\sin{x})$ where $a$ and $b$ are arbitrary constants, is

If $\frac{dy}{dx} = 2e^xy^3$, $y(0)= \frac{1}{2}$ then what is $4y^2(2-e^x)$ equal to?

A solution of the differential equation

$\left(\frac{d y}{d x}\right)^2-x \frac{d y}{d x}=0 $ is

Consider the following statements:

1. The degree of the differential equation $\frac{\text{dy}}{\text{dx}} + \cos \left(\frac{\text{dy}}{\text{dx}}\right)$ = 0 is 1.

2. The order of the differential equation $\left(\frac{\text{d}^2\text{y}}{\text{dx}^2}\right)^3 + \cos \left(\frac{\text{dy}}{\text{dx}}\right) $ = 0 is 2.

Which of the statements above is/are correct?

What is the degree of the following differential equation?

$\rm x=\sqrt{1+\frac{d^2y}{dx^2}}$

Which one of the following differential equations has the general solution y = ae^x + be^-x?

What is the solution of the following differential equation?

$\rm \ln\left(\frac{dy}{dx}\right)+y = x$