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Beliebt Rechnen >

(dy)/(dx)=(x/(2000))-(y/(5000)),y(0)=0

Lösung

\frac{d y}{d x} = (\frac{x}{2000}) - (\frac{y}{5000}), y (0) = 0

Lösung

y = \frac{5 ( x - 5000 )}{2} + \frac{12500}{e ^{\frac{x}{5000}}}

Schritte zur Lösung

\frac{d y}{d x} = (\frac{x}{2000}) - (\frac{y}{5000})

Solve linear ODE:

y = \frac{5 ( x - 5000 )}{2} + \frac{12500}{e ^{\frac{x}{5000}}}

y = \frac{5 ( x - 5000 )}{2} + \frac{12500}{e ^{\frac{x}{5000}}}

Graph

Beliebte Beispiele

limit as x approaches 5 of-((x+1)/(x-5))

x \to 5 lim (- (\frac{x + 1}{x - 5}))

integral of x/5

\int \frac{x}{5} d x

derivative of 5/(3x)

\frac{d}{d x} (\frac{5}{3 x})

tangent f(x)=((e^{2x}+1))/(e^x-2)

t an g e n t f (x) = \frac{( e ^{2 x} + 1 )}{e ^{x} - 2}

tangent x^4-3x^3+5

t an g e n t x^{4} - 3 x^{3} + 5