y^'=5y+y^6,y(0)=1

Lösung

y^{^{'}} = 5 y + y^{6}, y (0) = 1

y = 5 \frac{5 e ^{25 t}}{6 - e ^{25 t}}

Schritte zur Lösung

y^{'} (t) = 5 y + y^{6}

Solve Bernoulli ODE:

y = 5 \frac{5 e ^{25 t}}{6 - e ^{25 t}}

y = 5 \frac{5 e ^{25 t}}{6 - e ^{25 t}}

\int_{0}^{x} \frac{1}{t ^{2} + t + 1} d t

x \to 0 lim (sec (2 x))

in v erse l a pl a ce \frac{1}{s - 4}

\int \frac{( 7 - 4 x ^{3} + 6 x ^{6} )}{x ^{6}} d x

\frac{d}{d x} (x^{5} (2 x - 1)^{7})