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

Lösung

(x + 2)^{2} \frac{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

(x + 2)^{2} \frac{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}}

x \to 3 - lim (\frac{- 5}{x - 3})

d er i v a t i v e \frac{( - x ^{2} + 2 x + 2 )}{( x + 1 ) ^{4}}

y^{^{''}} + y^{^{'}} - 6 y = 2 e^{5 x}

\frac{\partial}{\partial x} (y e^{(x^{2} - y)})

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 0