(dy)/(dt)y=(4t-1)(3t-6)^{-1}

Lösung

\frac{d y}{d t} y = (4 t - 1) (3 t - 6)^{- 1}

y = \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}, y = - \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}

Schritte zur Lösung

\frac{d y}{d t} y = (4 t - 1) (3 t - 6)^{- 1}

Solve separable ODE:

y = \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}, y = - \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}

y = \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}, y = - \frac{c _{1} + 8 ( t + 2 ln ( 3 ( t - 2 ) ) - 2 ) - 2 ln ( 3 t - 6 )}{3}

t y^{^{'}} 2 y = t^{2} - t^{1}

y^{^{'}} - \frac{y}{( ln ( y ) ) ^{2}} = 0, y (0) = 1

\frac{d y}{d x} = y^{2} - 9 y + 20

y^{^{'}} = - \frac{y}{2} - 2

y^{^{'}} = - \frac{y}{2} - 3