Calculus 2: Separable differential equations

Solve the differential equation $\frac{dy}{dx} = \frac{x^2}{y^2}$ using separation of variables to find the general solution and the particular solution given the initial condition $y(1) = 2$.

Solve the differential equation $\frac{dy}{dx} = xy$ using separation of variables, given the initial condition $y(0) = 5$, and find both the general and particular solutions.

Solve the differential equation $\frac{dy}{dx} = y^2 + 1$ and find the general solution as well as the particular solution given the initial condition $y(1) = 0$.

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

Solve for $y$ given $\frac{dy}{dx} = \frac{6x^2}{2y + \cos(y)}$.

dy/dx = x^2y. Solve for y.

dy/dx = xe$y$. Given the initial condition $y(0) = 0$, solve for $y$.

Solve the separable differential equation $\frac{dY}{dX} = -\frac{X}{Y}e^{X^2}$ given the initial condition that the solution must pass through the point (0,1).

Solve the differential equation $x^2 + 1 \frac{dy}{dx} = x \cdot y$ by separating variables.

Verify that the solution to the exponential growth equation is $y = ce^{kt}$, where c is a constant.

Solve a first order differential equation using the method of separation of variables.

Solve the differential equation $y' = \frac{xy}{y^2 + 1}$ using separation of variables.

Solve the differential equation $\frac{dy}{dx} = 5x$.

Solve the differential equation $\frac{dy}{dx} = 3x^2 e^{-y}$ that satisfies the initial condition $y(0) = 0$.