展開する 1/x (x(dy}{dx}+3(y+x^2)=\frac{sin(x))/x)

解

展開する

\frac{1}{x} (x \frac{d y}{d x} + 3 (y + x^{2}) = \frac{sin ( x )}{x})

\frac{d y}{d x} + \frac{3 y}{x} + 3 x = \frac{sin ( x )}{x}

解答ステップ

\frac{1}{x} (x \frac{d y}{d x} + 3 (y + x^{2}) = \frac{sin ( x )}{x})

= \frac{1}{x} (x \frac{d y}{d x} + 3 = \frac{sin ( x )}{x} (y + x^{2}))

分配法則を適用する:

a (b + c) = ab + a c

a = \frac{1}{x}, b = x \frac{d y}{d x}, c = 3 (y + x^{2}) = \frac{sin ( x )}{x}

\frac{1}{x} x \frac{d y}{d x} + \frac{1}{x} \cdot 3 (y + x^{2}) = \frac{sin ( x )}{x}

\frac{1}{x} x \frac{d y}{d x} + 3 \cdot \frac{1}{x} (y + x^{2}) = \frac{sin ( x )}{x}

拡張

\frac{1}{x} x \frac{d y}{d x} + 3 \cdot \frac{1}{x} (y + x^{2}) : \frac{d y}{d x} + \frac{3 y}{x} + 3 x

\frac{d y}{d x} + \frac{3 y}{x} + 3 x = \frac{sin ( x )}{x}