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人気のある微分積分 >

ln(x)y^'-((2*sqrt(y))/x)=0

解

ln (x) y^{^{'}} - (\frac{2 \cdot y}{x}) = 0

解

y = ln^{2} (ln (x)) + c_{1} ln (ln (x)) + \frac{c _{1}^{2}}{4}

解答ステップ

ln (x) y^{'} (x) - (\frac{2 \cdot y}{x}) = 0

分離可能 ODE を解く:

y = ln^{2} (ln (x)) + c_{1} ln (ln (x)) + \frac{c _{1}^{2}}{4}

y = ln^{2} (ln (x)) + c_{1} ln (ln (x)) + \frac{c _{1}^{2}}{4}

グラフ

人気の例

(dx)/(dy)=sin(5x)

\frac{d x}{d y} = sin (5 x)

(dy)/(dx)y=ln(ln(ln(x)))

\frac{d y}{d x} y = ln (ln (ln (x)))

(dy)/(dt)=2tcos^2(y),y(0)= pi/4

\frac{d y}{d t} = 2 t cos^{2} (y), y (0) = \frac{π}{4}

(x+\H(x)x)dx+x(\H(x)dx+xd\H(x))=0

(x + H (x) x) d x + x (H (x) d x + x d H (x)) = 0

(dy)/(dx)=-x/(y^2)

\frac{d y}{d x} = - \frac{x}{y ^{2}}