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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
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Expand the fraction $\frac{1-y\sin\left(x\right)}{\cos\left(x\right)}$ into $2$ simpler fractions with common denominator $\cos\left(x\right)$
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$\frac{dy}{dx}=\frac{1}{\cos\left(x\right)}+\frac{-y\sin\left(x\right)}{\cos\left(x\right)}$
Learn how to solve problems step by step online. Solve the differential equation dy/dx=(1-sin(x)y)/cos(x). Expand the fraction \frac{1-y\sin\left(x\right)}{\cos\left(x\right)} into 2 simpler fractions with common denominator \cos\left(x\right). Rearrange the differential equation. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=\frac{\sin\left(x\right)}{\cos\left(x\right)} and Q(x)=\frac{1}{\cos\left(x\right)}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
