(y+x^3+xy^2)dx-(x)dy=0

解答

(y + x^{3} + x y^{2}) d x - (x) d y = 0

y = tan (\frac{x ^{2}}{2} + c_{1}) x

求解步骤

(y + x^{3} + x y^{2}) d x - (x) d y = 0

使用替代法求解:

y = tan (\frac{x ^{2}}{2} + c_{1}) x

y = tan (\frac{x ^{2}}{2} + c_{1}) x

\int \frac{18}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

n = 0 \sum \infty \frac{5 ^{n + 1}}{4 ^{n} ( 3 n - 1 ) !}

x \to 4 lim (- \frac{1}{x ^{\frac{3}{2}}})

\int e^{- x} 2 x d x

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