(3t^5+1)y(dy)/(dt)=4t^4

Lösung

(3 t^{5} + 1) y \frac{d y}{d t} = 4 t^{4}

y = \frac{8 ln ( 3 t ^{5} + 1 ) + c _{1}}{15}, y = - \frac{8 ln ( 3 t ^{5} + 1 ) + c _{1}}{15}

Schritte zur Lösung

(3 t^{5} + 1) y \frac{d y}{d t} = 4 t^{4}

Solve separable ODE:

y = \frac{8 ln ( 3 t ^{5} + 1 ) + c _{1}}{15}, y = - \frac{8 ln ( 3 t ^{5} + 1 ) + c _{1}}{15}

y = \frac{8 ln ( 3 t ^{5} + 1 ) + c _{1}}{15}, y = - \frac{8 ln ( 3 t ^{5} + 1 ) + c _{1}}{15}

\frac{d x}{d t} = \frac{1 - x ^{2}}{x t}

y^{^{'}} = \frac{x}{e ^{y}}

y^{^{'}} = \frac{x sin ( x )}{y}, y (0) = - 1

4 x y^{2} + (x^{2} + 1) y^{^{'}} = 0

d x = (8 x y + 3 y) d y