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Beliebt Rechnen >

sin(2x)dx+cos(8y)dy=0,y(pi/2)= pi/8

Lösung

sin (2 x) d x + cos (8 y) d y = 0, y (\frac{π}{2}) = \frac{π}{8}

Lösung

y = \frac{arcsin ( 4 cos ( 2 x ) + c _{1} )}{8} + \frac{πn}{4}, y = \frac{π}{8} + \frac{arcsin ( - 4 cos ( 2 x ) - c _{1} )}{8} + \frac{πn}{4}

Schritte zur Lösung

sin (2 x) d x + cos (8 y) d y = 0

Solve separable ODE:

y = \frac{arcsin ( 4 cos ( 2 x ) + c _{1} )}{8} + \frac{πn}{4}, y = \frac{π}{8} + \frac{arcsin ( - 4 cos ( 2 x ) - c _{1} )}{8} + \frac{πn}{4}

y = \frac{arcsin ( 4 cos ( 2 x ) + c _{1} )}{8} + \frac{πn}{4}, y = \frac{π}{8} + \frac{arcsin ( - 4 cos ( 2 x ) - c _{1} )}{8} + \frac{πn}{4}

Graph

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y^'-(2/x y)=((y^3)/(x^3)),y(1)=1

y^{^{'}} - (\frac{2}{x} y) = (\frac{y ^{3}}{x ^{3}}), y (1) = 1