Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Separable Differential Equation
- Exact Differential Equation
- Linear Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
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Divide all the terms of the differential equation by $\sin\left(x\right)$
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$\frac{dy}{dx}\frac{\sin\left(x\right)}{\sin\left(x\right)}+\frac{y\cos\left(x\right)}{\sin\left(x\right)}=\frac{x\sin\left(x\right)}{\sin\left(x\right)}$
Learn how to solve problems step by step online. Solve the differential equation sin(x)dy/dx+cos(x)y=xsin(x). Divide all the terms of the differential equation by \sin\left(x\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(x)=\frac{\cos\left(x\right)}{\sin\left(x\right)} and Q(x)=x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.
