(x+y)^2dx+(2xy+x^2-7)dy=0

解答

(x + y)^{2} d x + (2 x y + x^{2} - 7) d y = 0

y = \frac{21 - 3 x ^{2} + 441 - 126 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{21 - 3 x ^{2} - 441 - 126 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

求解步骤

(x + y)^{2} d x + (2 x y + x^{2} - 7) d y = 0

求解恰当方程:

y = \frac{21 - 3 x ^{2} + 441 - 126 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{21 - 3 x ^{2} - 441 - 126 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

y = \frac{21 - 3 x ^{2} + 441 - 126 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}, y = \frac{21 - 3 x ^{2} - 441 - 126 x ^{2} - 3 x ^{4} + 36 c _{1} x}{6 x}

a re a 1 - x^{2}, x^{2} - 1

d er i v a t i v e f (x) = 2 x^{2} + 4 x + 3

(t^{2} + 25) \frac{d y}{d t} + 2 t y = t^{2} (t^{2} + 25)

in v erse l a pl a ce \frac{( 2 s + 2.5 )}{( s + 0.5 )}

p a r i t y ln (csc (x) - cot (x))