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...
Rewrite the differential equation
Learn how to solve problems step by step online.
$\frac{dy}{dx}=\frac{\frac{x}{\cos\left(\frac{y}{x}\right)}+y}{x}$
Learn how to solve problems step by step online. Solve the differential equation xdy/dx=x/cos(y/x)+y. Rewrite the differential equation. Combine \frac{x}{\cos\left(\frac{y}{x}\right)}+y in a single fraction. Divide fractions \frac{\frac{x+y\cos\left(\frac{y}{x}\right)}{\cos\left(\frac{y}{x}\right)}}{x} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. We can identify that the differential equation \frac{dy}{dx}=\frac{x+y\cos\left(\frac{y}{x}\right)}{x\cos\left(\frac{y}{x}\right)} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree.
