(cos(x)sin(x)-xy^22)dx+y(1-x^2)dy=0

Lösung

(cos (x) sin (x) - x y^{2} 2) d x + y (1 - x^{2}) d y = 0

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

Schritte zur Lösung

(cos (x) sin (x) - x y^{2} 2) d x + y (1 - x^{2}) d y = 0

Solve Bernoulli ODE:

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

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

d er i v a t i v e \frac{3 x}{2 - cot ( x )}

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\int_{t - 1}^{t} (1 - t + x) \cdot x d x

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