y^'=y(xy^4+3)

Lösung

y^{^{'}} = y (x y^{4} + 3)

y = 4 \frac{36 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}, y = - 4 \frac{36 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}

Schritte zur Lösung

y^{'} (x) = y (x y^{4} + 3)

Solve Bernoulli ODE:

y = 4 \frac{36 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}, y = - 4 \frac{36 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}

y = 4 \frac{36 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}, y = - 4 \frac{36 e ^{12 x}}{- 12 x e ^{12 x} + e ^{12 x} + c _{1}}

y^{^{'}} - \frac{2 y}{x} = 1

9^{^{'}}

x \to - \infty lim (\frac{( 1 - 1 ) ^{e - x} + ( 2 - 2 ) x ^{4} + 1}{x ^{2}})

x \to 0 lim (\frac{x 2 ^{x}}{2 x - 1})

x \to \infty + lim (\frac{5 - 2 x}{3 x - 7})