Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
- Load more...
Rearrange the differential equation
Learn how to solve integrals of rational functions problems step by step online.
$\frac{dy}{dx}-\left(y+5e^{\frac{x}{2}}\cos\left(5x\right)\right)=-\frac{1}{2}e^{\frac{x}{2}}\sin\left(5x\right)$
Learn how to solve integrals of rational functions problems step by step online. Solve the differential equation dy/dx=-1/2e^(x/2)sin(5x)+5e^(x/2)cos(5x)y. 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)=-1 and Q(x)=-\frac{1}{2}e^{\frac{x}{2}}\sin\left(5x\right). 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.
