xsin(y)dx+(x^2+1)cos(y)dy=0

解

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

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

解答ステップ

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

分離可能 ODE を解く:

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

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