y^'-2xy=x^3y^5

Lösung

y^{^{'}} - 2 x y = x^{3} y^{5}

y = 4 \frac{8 e ^{4 x^{2}}}{- 4 x ^{2} e ^{4 x^{2}} + e ^{4 x^{2}} + c _{1}}, y = - 4 \frac{8 e ^{4 x^{2}}}{- 4 x ^{2} e ^{4 x^{2}} + e ^{4 x^{2}} + c _{1}}

Schritte zur Lösung

y^{'} (x) - 2 x y = x^{3} y^{5}

Solve Bernoulli ODE:

y = 4 \frac{8 e ^{4 x^{2}}}{- 4 x ^{2} e ^{4 x^{2}} + e ^{4 x^{2}} + c _{1}}, y = - 4 \frac{8 e ^{4 x^{2}}}{- 4 x ^{2} e ^{4 x^{2}} + e ^{4 x^{2}} + c _{1}}

y = 4 \frac{8 e ^{4 x^{2}}}{- 4 x ^{2} e ^{4 x^{2}} + e ^{4 x^{2}} + c _{1}}, y = - 4 \frac{8 e ^{4 x^{2}}}{- 4 x ^{2} e ^{4 x^{2}} + e ^{4 x^{2}} + c _{1}}

\int x 9 - x d x

d er i v a t i v e \frac{y ^{2} + x ^{2}}{y ^{2} - x ^{2}}

t an g e n t f (x) = \frac{2}{x}, at x = 1

t an g e n t x^{2} - 3 x + 3

\int 2 y e^{2 z} d z