ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

(dy)/(dx)=y^2-9

解

\frac{d y}{d x} = y^{2} - 9

解

y = \frac{3 e ^{6 c_{1}}}{e ^{6 x} - e ^{6 c_{1}}} + \frac{3 e ^{6 x}}{e ^{6 x} - e ^{6 c_{1}}}

解答ステップ

\frac{d y}{d x} = y^{2} - 9

代用

\frac{d y}{d x}

と

y^{'} (x)

y^{^{'}} (x) = y^{2} - 9

x

を解く

y^{'} (x) = \frac{d y}{d x} = \frac{1}{\frac{d x}{d y}} = \frac{1}{x ^{^{'}}}

(\frac{1}{x ^{^{^{'}}}}) = y^{2} - 9

分離する

x^{^{'}} : x^{^{'}} = \frac{1}{y ^{2} - 9}

f^{^{'}} (x) = g (x)

であれば

f (x) = \int g (x) d x

x = \int \frac{1}{y ^{2} - 9} d y

\int \frac{1}{y ^{2} - 9} d y = - \frac{1}{6} (ln (\frac{y}{3} + 1) - ln (\frac{y}{3} - 1)) + c_{1}

x = - \frac{1}{6} (ln (\frac{y}{3} + 1) - ln (\frac{y}{3} - 1)) + c_{1}

分離する

y : y = \frac{3 e ^{6 c_{1}}}{e ^{6 x} - e ^{6 c_{1}}} + \frac{3 e ^{6 x}}{e ^{6 x} - e ^{6 c_{1}}}

y = \frac{3 e ^{6 c_{1}}}{e ^{6 x} - e ^{6 c_{1}}} + \frac{3 e ^{6 x}}{e ^{6 x} - e ^{6 c_{1}}}

グラフ

人気の例

derivative of 5x^3+x^2+1/x

\frac{d}{d x} (5 x^{3} + x^{2} + \frac{1}{x})

derivative of 2(5-9x^5)

\frac{d}{d x} (2 (5 - 9 x)^{5})

integral of (1-x)/(1-x^2)

\int \frac{1 - x}{1 - x ^{2}} d x

integral from 0 to 2 of (x^2-2x)

\int_{0}^{2} (x^{2} - 2 x) d x

integral of sin^2(x+4)

\int sin^{2} (x + 4) d x