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Beliebt Rechnen >

x^2(dy)/(dx)+4xy-e^x=0

Lösung

x^{2} \frac{d y}{d x} + 4 x y - e^{x} = 0

Lösung

y = \frac{e ^{x}}{x ^{2}} - \frac{2 ( e ^{x} x - e ^{x} )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

Schritte zur Lösung

x^{2} \frac{d y}{d x} + 4 x y - e^{x} = 0

Solve linear ODE:

y = \frac{e ^{x}}{x ^{2}} - \frac{2 ( e ^{x} x - e ^{x} )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

y = \frac{e ^{x}}{x ^{2}} - \frac{2 ( e ^{x} x - e ^{x} )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

Graph

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