Final answer to the problem
$\ln\left|\csc\left(y\right)+\cot\left(y\right)\right|=\frac{x^{3}}{3}+C_0$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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1
Rewrite the differential equation using Leibniz notation
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$\frac{dy}{dx}=-x^2\sin\left(y\right)$
Learn how to solve problems step by step online. Solve the differential equation y^'=-x^2sin(y). Rewrite the differential equation using Leibniz notation. 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. Simplify the expression \frac{1}{\sin\left(y\right)}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Final answer to the problem
$\ln\left|\csc\left(y\right)+\cot\left(y\right)\right|=\frac{x^{3}}{3}+C_0$
