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- Exact Differential Equation
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- Integrate by partial fractions
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Rewrite the differential equation
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$\frac{dy}{dx}=\frac{x\cos\left(\frac{y}{x}\right)+y}{x}$
Learn how to solve problems step by step online. Solve the differential equation xdy/dx=xcos(y/x)+y. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{x\cos\left(\frac{y}{x}\right)+y}{x} 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. Use the substitution: y=ux. Expand and simplify.