((x+2)^{(2)}(dy))/((dx))=5-8y-4xy

Lösung

\frac{( x + 2 ) ^{(2)} ( d y )}{( d x )} = 5 - 8 y - 4 x y

y = \frac{5 ( x ^{3} + 6 x ^{2} + 12 x )}{3 ( 16 + 32 x + 24 x ^{2} + 8 x ^{3} + x ^{4} )} + \frac{c _{1}}{16 + 32 x + 24 x ^{2} + 8 x ^{3} + x ^{4}}

Schritte zur Lösung

\frac{( x + 2 ) ^{(2)} ( d y )}{( d x )} = 5 - 8 y - 4 x y

Solve linear ODE:

y = \frac{5 ( x ^{3} + 6 x ^{2} + 12 x )}{3 ( 16 + 32 x + 24 x ^{2} + 8 x ^{3} + x ^{4} )} + \frac{c _{1}}{16 + 32 x + 24 x ^{2} + 8 x ^{3} + x ^{4}}

y = \frac{5 ( x ^{3} + 6 x ^{2} + 12 x )}{3 ( 16 + 32 x + 24 x ^{2} + 8 x ^{3} + x ^{4} )} + \frac{c _{1}}{16 + 32 x + 24 x ^{2} + 8 x ^{3} + x ^{4}}

\int \frac{( y - 2 )}{y + 3} d y

\int_{0}^{0.6} 2 x e^{- x} d x

y^{^{'}} = 2 y

\frac{d y}{d x} = y^{\frac{1}{3}}

t an g e n t x^{2} + 11, at x = 5