sin(2x)dx+cos(7y)dy=0,y(pi^2)=pi^7

解

sin (2 x) d x + cos (7 y) d y = 0, y (π^{2}) = π^{7}

y = \frac{arcsin ( \frac{7}{2} cos ( 2 x ) + c _{1} )}{7} + \frac{2 πn}{7}, y = \frac{π}{7} + \frac{arcsin ( - \frac{7}{2} cos ( 2 x ) - c _{1} )}{7} + \frac{2 πn}{7}

解答ステップ

sin (2 x) d x + cos (7 y) d y = 0

分離可能 ODE を解く:

y = \frac{arcsin ( \frac{7}{2} cos ( 2 x ) + c _{1} )}{7} + \frac{2 πn}{7}, y = \frac{π}{7} + \frac{arcsin ( - \frac{7}{2} cos ( 2 x ) - c _{1} )}{7} + \frac{2 πn}{7}

y = \frac{arcsin ( \frac{7}{2} cos ( 2 x ) + c _{1} )}{7} + \frac{2 πn}{7}, y = \frac{π}{7} + \frac{arcsin ( - \frac{7}{2} cos ( 2 x ) - c _{1} )}{7} + \frac{2 πn}{7}