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人気のある微分積分 >

(dy}{dx}=\frac{(1-3y)^2)/x ,y(1)=1

解

\frac{d y}{d x} = \frac{( 1 - 3 y ) ^{2}}{x}, y (1) = 1

解

y = - \frac{2 ln ( x )}{- 6 ln ( x ) + 1} + \frac{1}{- 6 ln ( x ) + 1}

解答ステップ

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

分離可能 ODE を解く:

y = - \frac{2 ln ( x )}{- 6 ln ( x ) + 1} + \frac{1}{- 6 ln ( x ) + 1}

y = - \frac{2 ln ( x )}{- 6 ln ( x ) + 1} + \frac{1}{- 6 ln ( x ) + 1}

グラフ

人気の例

derivative of (x^2+1^2)

\frac{d}{d x} ((x^{2} + 1)^{2})

sum from n=0 to infinity of (n^2)/(n!)

n = 0 \sum \infty \frac{n ^{2}}{n !}

derivative of sin(3xln(sech(2x)))

\frac{d}{d x} (sin (3 x) ln (sech (2 x)))

(\partial)/(\partial y)(ln(x^2+y^2+2))

\frac{\partial}{\partial y} (ln (x^{2} + y^{2} + 2))

sum from n=1 to infinity of (x^n)/(1^n)

n = 1 \sum \infty \frac{x ^{n}}{1 ^{n}}