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- Exact Differential Equation
- Linear Differential Equation
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- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
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Divide all the terms of the differential equation by $\cos\left(t\right)$
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$\frac{dy}{dt}\frac{\cos\left(t\right)}{\cos\left(t\right)}+\frac{y\sin\left(t\right)}{\cos\left(t\right)}=\frac{1}{\cos\left(t\right)}$
Learn how to solve problems step by step online. Solve the differential equation cos(t)dy/dt+sin(t)y=1. Divide all the terms of the differential equation by \cos\left(t\right). 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(t)=\frac{\sin\left(t\right)}{\cos\left(t\right)} and Q(t)=\frac{1}{\cos\left(t\right)}. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(t), we first need to calculate \int P(t)dt.
