(1-5y+x)y^'+y=5x-1

Lösung

(1 - 5 y + x) y^{^{'}} + y = 5 x - 1

y = - \frac{- 1 - x + - 24 x ^{2} + 12 x + 1 - c _{1}}{5}, y = \frac{x + - 24 x ^{2} + 12 x + 1 - c _{1} + 1}{5}

Schritte zur Lösung

(1 - 5 y + x) y^{'} (x) + y = 5 x - 1

Solve exact ODE:

y = - \frac{- 1 - x + - 24 x ^{2} + 12 x + 1 - c _{1}}{5}, y = \frac{x + - 24 x ^{2} + 12 x + 1 - c _{1} + 1}{5}

y = - \frac{- 1 - x + - 24 x ^{2} + 12 x + 1 - c _{1}}{5}, y = \frac{x + - 24 x ^{2} + 12 x + 1 - c _{1} + 1}{5}

(\frac{1}{x})^{^{'}}

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\frac{d y}{d x} = e^{2 y} sin (3 x)