CUET Mathematics: CalculusDifferential Equations. Free, no login required.

Order and degree of the differential equation $y\frac{dy}{dx} + \frac{4}{\frac{dy}{dx}} = 5$ are

Solution of the differential equation $(x + xy)dy - y(1 - x^2)dx = 0$ is

The integrating factor of the differential equation $\cos x \frac{dy}{dx} + y\sin x = 1$ is

The order and degree of the differential equation $\left[\left(\frac{d^2y}{dx^2}\right)^2 - 3\right]^{\frac{1}{3}} = 2\left(\frac{dy}{dx}\right)^{\frac{1}{4}}$ are

Integrating factor of the differential equation $\frac{dy}{dx} - \frac{1}{x} y = 1$ is:

The order and the degree of the differential equation $\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 = 2x^2 \log\left(\frac{d^2y}{dx^2}\right)$ are respectively:

Match List I with List II.

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The number of arbitrary constants in the general solution of a differential equation of fourth order is:

The solution of differential equation $y(1 - x^2)\frac{dy}{dx} = x(1 + y^2)$ is :

The integrating factor of the differential equation $x\frac{dy}{dx} - y = 2x^2$ is :

Match List - I with List - II

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Choose the correct statements:

A. The order and degree (if defined) of a differential equation are always positive integrals

B. The order of a differential equation is the highest order derivative of the dependent variable with respect to the independent variable involved in a differential equation

C. If $\frac{dy}{dx} + P(x)y = Q(x)$ then Integrating factor $= e^{\int P(x)dx}$

D. The sum of order and degree of differential equation $1 + (y'')^5 = (y''')^3$ is $8$

E. If the solution of a differential equation of order $n$, contains $n$ arbitrary constant, then it is called a general solution

Choose the correct answer from the options given below:

The differential equation $\frac{dy}{dx} + \frac{x}{y} = 0$, represents the family of curves:

The degree of the differential equation

$\left(1 + \frac{dy}{dx}\right)^4 = \left(\frac{d^2y}{dx^2}\right)^2$ is:

Solution of $\frac{dy}{dx} = (1+x^2)(1+y^2)$ is:

Particular solution of the differential equation $\log\left(\frac{dy}{dx}\right) = x + y$, given that when $x = 0, y = 0$ is:

The solution of the differentiable equation $2x\frac{dy}{dx} + y = 14x^3, x > 0$, is