Differential Equations

The order of the differential equation $y = c_1 + c_2 e^x$ is:

The degree of the differential equation $\frac{d^2y}{dx^2} = \log x$ is:

The order of the differential equation representing $y = A e^x + B e^{-x} + C$ is:

The degree of $\frac{dy}{dx} = \sin x$ is:

Find the differential equation representing the family of curves $y = a e^x + b e^{2x} + c$, where $a, b,$ and $c$ are arbitrary constants.

What is the order of the differential equation whose general solution is given by $y = c_1 \cos^2 x + c_2 \sin^2 x + c_3 \cos(2x + c_4)$, where $c_1, c_2, c_3, c_4$ are arbitrary constants?

The degree of the differential equation $\frac{d^2y}{dx^2} + y = \sqrt[4]{x + \left(\frac{d^2y}{dx^2}\right)^2}$ is:

The particular solution of the differential equation $x^{2} dy + y(x+y) dx = 0$, given that $y(1) = 1$, is:

The order and degree of the differential equation $y''' + 2(y'')^{2} + y' = 0$ are:

The general solution of $\frac{dy}{dx} = \cos(x+y)$ is:

Find the general solution of $\frac{dy}{dx} = \frac{1}{x+3}$.

Solve $\frac{dy}{dx} = 3x^2 y$.

The solution of the differential equation $\frac{dy}{dx} = \frac{1}{2y}$ is:

Find the solution of $\frac{dy}{dx} = \frac{x}{y-5}$.

Find the particular solution of $\frac{dy}{dx} = y^2$ given that $y = -1$ when $x = 1$.

The general solution of $(e^y - e^{-y}) dy = (1/x - x) dx$ is:

Find the general solution of $\frac{dy}{dx} = \frac{y(x+1)}{x(y+1)}$.

The general solution of $\frac{dy}{dx} = y \log x$ is:

Solve the differential equation $\frac{dy}{dx} = \frac{x+y-1}{x+y+1}$.

Find the general solution of $\log(\frac{dy}{dx}) = 3x+4y$.

What is the degree of the function $f(x, y) = \frac{x+y}{x^2+y^2}$?

Which of these is a homogeneous differential equation of first degree (degree 1 for $M, N$)?

The function $f(x, y) = \frac{x^2+y^2}{xy}$ is homogeneous of degree:

If $\frac{dy}{dx} = g\left(\frac{y}{x}\right)$, then $\int \frac{dv}{g(v)-v} = ...$

Solve the differential equation $x^2 y dx - (x^3+y^3) dy = 0$.

Find the solution of $(x^2+3xy) dy = (y^2+3xy) dx$.

Solve the differential equation $\frac{dy}{dx} = \frac{y}{x} + \tan\left(\frac{y}{x}\right)$.

Solve: $x \frac{dy}{dx} = y + x \frac{1 + (y/x)^2}{2(y/x)}$.

Find the general solution of $(x^4 + y^4)dx - 2x^3y dy = 0$.

Solve the differential equation: $\frac{dy}{dx} = \frac{2x^3y}{x^4 + y^4}$.

The integrating factor for $\frac{dx}{dy} + x \sec^2 y = 1$ is:

The integrating factor of $\frac{dy}{dx} + y (2^x \ln 2) = 1$ is:

Find the integrating factor for $\frac{dy}{dx} + \frac{y}{\sqrt{x}} = 1$.

What is the integrating factor of $\frac{dx}{dy} + x \cot y = e^y$?

Find the general solution of the differential equation $x \frac{dy}{dx} + y = x \ln x$.

The general solution of the differential equation $\frac{dy}{dx} + y = \frac{1}{1+e^x}$ is:

The general solution of $\frac{dx}{dy} + \frac{x}{y} = y+1$ is:

The integrating factor of $\frac{dy}{dx} + y \frac{1}{x \log x} = \frac{1}{x}$ is:

The general solution of the differential equation $\frac{dx}{dy} + x \cot y = 2y + y^2 \cot y$ is:

Find the solution of $x \frac{dy}{dx} + 2y = x^2$ given $y(1) = 0$.

The degree of a differential equation is the power of the ______ order derivative when the equation is a polynomial in derivatives.

Which of the following is the order of the differential equation $\frac{dy}{dx} = e^x$?

The order of the differential equation $\frac{d^2y}{dx^2} = \sqrt[3]{1 + \frac{dy}{dx}}$ is:

What is the degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^3 + y = 0$?

Find the order of the differential equation $y = c_1 e^x + c_2 e^{x+c_3}$.

The degree of the differential equation $\log\left(\frac{dy}{dx}\right) = ax + by$ is:

What is the order of the differential equation of all lines at a constant distance $p$ from the origin?

The degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + e^{\frac{dy}{dx}} = 0$ is:

Determine the number of arbitrary constants in the general solution of the differential equation representing the family of circles passing through the origin.

Find the sum of the order and the degree of the differential equation $y^{(iv)} - \sin(y''') = 0$.

What is the degree of the differential equation: $\frac{d^2y}{dx^2} + y = \log\left(\frac{dy}{dx}\right)$?

The degree of the differential equation $\left(\frac{dy}{dx}\right)^3 = 4x$ is:

Find the degree of the differential equation: $e^{y'''} - x y'' + y = 0$.

What is the degree of the differential equation: $\frac{d^3y}{dx^3} + \left(\frac{d^2y}{dx^2}\right)^4 + \frac{dy}{dx} + y = 0$?

The degree of the differential equation $y' + y = \int y dx$ is:

Determine the degree of the differential equation: $y''' + \sin(y''') = 5$.

The degree of the differential equation $y'' + (y')^3 = x^2$ is:

Find the degree of the differential equation $\frac{d^2y}{dx^2} + \sqrt{y} = 0$.

Identify the degree of the differential equation $\left( \frac{d^3y}{dx^3} \right)^2 + y'' = \sqrt{y'}$.

What is the degree of the differential equation $x = \sin \left( \frac{dy}{dx} - y \right)$?