What is the solution for (y+xcos^2(y/x))dx-xdy=0 ?

The solution for (y+xcos^2(y/x))dx-xdy=0 is y=arctan(ln(x)+c_{1})x+pinx

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(y+xcos^2(y/x))dx-xdy=0

(y + x cos^{2} (\frac{y}{x})) d x - x d y = 0

y = arctan (ln (x) + c_{1}) x + πn x

Solution steps

(y + x cos^{2} (\frac{y}{x})) d x - x d y = 0

Solve using substitution:

y = arctan (ln (x) + c_{1}) x + πn x

y = arctan (ln (x) + c_{1}) x + πn x

\int \frac{6 x}{1 + x ^{4}} d x

\frac{d x}{d t} = 349.344897 (1 - e^{- 0.0916 t})

\int (3 e^{- 0.4 x}) d x

\int 4 sin (x) - 1 + 8 x^{- 5} d x

f (- 3) = 20 x^{4}

What is the solution for (y+xcos^2(y/x))dx-xdy=0 ?
The solution for (y+xcos^2(y/x))dx-xdy=0 is y=arctan(ln(x)+c_{1})x+pinx