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Beliebt Rechnen >

(dx)/(dt)=-(sqrt(x))/(50pi)

Lösung

\frac{d x}{d t} = - \frac{x}{50 π}

Lösung

x = \frac{t ^{2}}{10000 π ^{2}} + \frac{c _{1} t}{5000 π ^{2}} + \frac{c _{1}^{2}}{10000 π ^{2}}

Schritte zur Lösung

\frac{d x}{d t} = - \frac{x}{50 π}

Solve separable ODE:

x = \frac{t ^{2}}{10000 π ^{2}} + \frac{c _{1} t}{5000 π ^{2}} + \frac{c _{1}^{2}}{10000 π ^{2}}

x = \frac{t ^{2}}{10000 π ^{2}} + \frac{c _{1} t}{5000 π ^{2}} + \frac{c _{1}^{2}}{10000 π ^{2}}

Graph

Beliebte Beispiele

(dy)/(dx)=((x+2))/((2y))

\frac{d y}{d x} = \frac{( x + 2 )}{( 2 y )}

x^2(dy)/(dx)+xy=3x

x^{2} \frac{d y}{d x} + x y = 3 x

(dy)/(dx)=(3x^2-2x)/(2y+1),y(0)=2

\frac{d y}{d x} = \frac{3 x ^{2} - 2 x}{2 y + 1}, y (0) = 2

y^{^{'}} = y + y^{2}

y^'=t*e^y,y(2)=0

y^{^{'}} = t \cdot e^{y}, y (2) = 0