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人気のある微分積分 >

x^'=1-3x+x^2

解

x^{^{'}} = 1 - 3 x + x^{2}

解

x = - \frac{3 e ^{5 c_{1}}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{5 e ^{5 c_{1}}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{3 e ^{5 t}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{5 e ^{5 t}}{2 ( e ^{5 t} - e ^{5 c_{1}} )}

解答ステップ

x^{'} (t) = 1 - 3 x + x^{2}

t

を解く

x^{'} (t) = \frac{d x}{d t} = \frac{1}{\frac{d t}{d x}} = \frac{1}{t ^{^{'}}}

(\frac{1}{t ^{^{^{'}}}}) = 1 - 3 x + x^{2}

分離する

t^{^{'}} : t^{^{'}} = \frac{1}{1 - 3 x + x ^{2}}

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

であれば

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

t = \int \frac{1}{1 - 3 x + x ^{2}} d x

\int \frac{1}{1 - 3 x + x ^{2}} d x = - \frac{1}{5} (ln (\frac{2 x - 3}{5} + 1) - ln (\frac{2 x - 3}{5} - 1)) + c_{1}

t = - \frac{1}{5} (ln (\frac{2 x - 3}{5} + 1) - ln (\frac{2 x - 3}{5} - 1)) + c_{1}

分離する

x : x = - \frac{3 e ^{5 c_{1}}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{5 e ^{5 c_{1}}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{3 e ^{5 t}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{5 e ^{5 t}}{2 ( e ^{5 t} - e ^{5 c_{1}} )}

x = - \frac{3 e ^{5 c_{1}}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{5 e ^{5 c_{1}}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{3 e ^{5 t}}{2 ( e ^{5 t} - e ^{5 c_{1}} )} + \frac{5 e ^{5 t}}{2 ( e ^{5 t} - e ^{5 c_{1}} )}

グラフ

人気の例

u^'=3e^{8x-\H(x)}

u^{^{'}} = 3 e^{8 x - H (x)}

y^'=((3x^2+4x-4))/(2y-4),y(1)=3

y^{^{'}} = \frac{( 3 x ^{2} + 4 x - 4 )}{2 y - 4}, y (1) = 3

xydy=(1+y^2)dx,y(2)=3

x y d y = (1 + y^{2}) d x, y (2) = 3

y - 3 y^{^{'}} = 1

y^5(dy)/(dx)=3x^3y^6-9x^3

y^{5} \frac{d y}{d x} = 3 x^{3} y^{6} - 9 x^{3}