(dy)/(dx)y=ln^8(sqrt((4+x^2)/(4-x^2)))

Lösung

\frac{d y}{d x} y = ln^{8} (\frac{4 + x ^{2}}{4 - x ^{2}})

y = 2 \cdot \int \frac{1}{256} ln^{8} (\frac{4 + x ^{2}}{4 - x ^{2}}) d x, y = - 2 \cdot \int \frac{1}{256} ln^{8} (\frac{4 + x ^{2}}{4 - x ^{2}}) d x

Schritte zur Lösung

\frac{d y}{d x} y = ln^{8} (\frac{4 + x ^{2}}{4 - x ^{2}})

Solve separable ODE:

y = 2 \cdot \int \frac{1}{256} ln^{8} (\frac{4 + x ^{2}}{4 - x ^{2}}) d x, y = - 2 \cdot \int \frac{1}{256} ln^{8} (\frac{4 + x ^{2}}{4 - x ^{2}}) d x

y = 2 \cdot \int \frac{1}{256} ln^{8} (\frac{4 + x ^{2}}{4 - x ^{2}}) d x, y = - 2 \cdot \int \frac{1}{256} ln^{8} (\frac{4 + x ^{2}}{4 - x ^{2}}) d x

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

y \frac{d y}{d x} = \frac{x}{( x + 1 )}

\frac{d y}{d x} = - 4 x y^{2}, y (0) = 1

\frac{d P}{d t} = - e^{- t} P, P (0) = 100

y^{^{'}} = y^{\frac{1}{5}}