2sin(3x)sin(2y)dy=3cos(3x)cos(2y)dx

解

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

y = \frac{arccos ( \frac{c _{1}}{s i n ( 3 x )} )}{2} + πn, y = - \frac{arccos ( \frac{c _{1}}{s i n ( 3 x )} )}{2} + πn

解答ステップ

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

分離可能 ODE を解く:

y = \frac{arccos ( \frac{c _{1}}{s i n ( 3 x )} )}{2} + πn, y = - \frac{arccos ( \frac{c _{1}}{s i n ( 3 x )} )}{2} + πn

y = \frac{arccos ( \frac{c _{1}}{s i n ( 3 x )} )}{2} + πn, y = - \frac{arccos ( \frac{c _{1}}{s i n ( 3 x )} )}{2} + πn