e^x(dy)/(dx)+y^3=xy^3,y=1,x=0

Lösung

e^{x} \frac{d y}{d x} + y^{3} = x y^{3}, y = 1, x = 0

y = \frac{e ^{x}}{2 x + e ^{x}}

Schritte zur Lösung

e^{x} \frac{d y}{d x} + y^{3} = x y^{3}

Solve separable ODE:

y = \frac{e ^{x}}{2 x + e ^{x}}

y = \frac{e ^{x}}{2 x + e ^{x}}

\frac{d y}{d x} = y (2 x - 3)

y^{^{'}} = e^{4 x - 5 y}

y^{^{'}} = \frac{6 e ^{2 x}}{e ^{y}}

y^{^{'}} = \frac{1 + x}{y}, y (0) = 5

y^{^{'}} sin (y) = 1