(dy)/(dx)=4x^3y,y(1)=e

Lösung

\frac{d y}{d x} = 4 x^{3} y, y (1) = e

y = e^{x^{4}}

Schritte zur Lösung

\frac{d y}{d x} = 4 x^{3} y

Solve separable ODE:

y = e^{x^{4}}

y = e^{x^{4}}

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

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

\frac{d y}{d x} = \frac{x ^{2}}{y + 1}

\frac{d y}{d x} = \frac{x + 2}{2 y}

y^{^{'}} - 2 x y^{3} = 0, y (2) = 1