sin(2x)dx+cos(3y)dy=0,y(pi/2)=(pi/3)

解

sin (2 x) d x + cos (3 y) d y = 0, y (\frac{π}{2}) = (\frac{π}{3})

y = \frac{arcsin ( \frac{3}{2} cos ( 2 x ) + c _{1} )}{3} + \frac{2 πn}{3}, y = \frac{π}{3} + \frac{arcsin ( - \frac{3}{2} cos ( 2 x ) - c _{1} )}{3} + \frac{2 πn}{3}

解答ステップ

sin (2 x) d x + cos (3 y) d y = 0

分離可能 ODE を解く:

y = \frac{arcsin ( \frac{3}{2} cos ( 2 x ) + c _{1} )}{3} + \frac{2 πn}{3}, y = \frac{π}{3} + \frac{arcsin ( - \frac{3}{2} cos ( 2 x ) - c _{1} )}{3} + \frac{2 πn}{3}

y = \frac{arcsin ( \frac{3}{2} cos ( 2 x ) + c _{1} )}{3} + \frac{2 πn}{3}, y = \frac{π}{3} + \frac{arcsin ( - \frac{3}{2} cos ( 2 x ) - c _{1} )}{3} + \frac{2 πn}{3}