(dy}{dx}=\frac{5x*sec(y/x)+y)/x

解

\frac{d y}{d x} = \frac{5 x \cdot sec ( \frac{y}{x} ) + y}{x}

y = arcsin (5 ln (x) + c_{1}) x + 2 πn x, y = π x + arcsin (- 5 ln (x) - c_{1}) x + 2 πn x

解答ステップ

\frac{d y}{d x} = \frac{5 x \cdot sec ( \frac{y}{x} ) + y}{x}

置換を使用して解く:

y = arcsin (5 ln (x) + c_{1}) x + 2 πn x, y = π x + arcsin (- 5 ln (x) - c_{1}) x + 2 πn x

y = arcsin (5 ln (x) + c_{1}) x + 2 πn x, y = π x + arcsin (- 5 ln (x) - c_{1}) x + 2 πn x