(6x^2+y-1)dx-(14y-x)dy=0,y(1)=0

Lösung

(6 x^{2} + y - 1) d x - (14 y - x) d y = 0, y (1) = 0

y = - \frac{- x + x ^{2} + 28 ( 2 x ^{3} - x - c _{1} )}{14}, y = - \frac{- x - x ^{2} + 28 ( 2 x ^{3} - x - c _{1} )}{14}

Schritte zur Lösung

(6 x^{2} + y - 1) d x - (14 y - x) d y = 0

Solve exact ODE:

y = - \frac{- x + x ^{2} + 28 ( 2 x ^{3} - x - c _{1} )}{14}, y = - \frac{- x - x ^{2} + 28 ( 2 x ^{3} - x - c _{1} )}{14}

y = - \frac{- x + x ^{2} + 28 ( 2 x ^{3} - x - c _{1} )}{14}, y = - \frac{- x - x ^{2} + 28 ( 2 x ^{3} - x - c _{1} )}{14}

x^{2} \frac{d y}{d x} + 2 x y = 2 x

d er i v a t i v e \frac{x}{6 x + 2}

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

\int \frac{1}{1 + 2 x ^{2} + x ^{4}} d x

in v erse l a pl a ce \frac{4 + s}{s ^{2} + 3 s + 1}