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Exercise

$cscy\:dx\:+\:sec^2\:dy\:=\:0$

Step-by-step Solution

Learn how to solve integral calculus problems step by step online. Solve the differential equation csc(ydx)+sec(dy)^2=0. Group the terms of the equation. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{2}{y}dy and replace the result in the differential equation.
Solve the differential equation csc(ydx)+sec(dy)^2=0

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Final answer to the exercise

$y=\sqrt{C_1e^{-x}},\:y=-\sqrt{C_1e^{-x}}$

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  • Exact Differential Equation
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Similar Questions Solved

$\frac{dy}{dx}=y^2-9$

$\frac{dy}{dx}=y^2-4$

$\frac{dy}{dx}=y-y^2$

$\frac{dy}{dx}=y\left(y+2\right)$

$\frac{dy}{dx}=\left(1+e^{-x}\right)\left(y^2-1\right)$

$\frac{dy}{dx}=\frac{x}{2x-y}$

$\frac{dy}{dx}=\frac{x+3y}{x-y}$

Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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