展开 2x(ye^{x^2}-1)dx+e^{x^2}dy

解答

展开

2 x (y e^{x^{2}} - 1) d x + e^{x^{2}} d y

2 e^{x^{2}} x y d x - 2 x d x + e^{x^{2}} d y

求解步骤

2 x (y e^{x^{2}} - 1) d x + e^{x^{2}} d y

= 2 x (e^{x^{2}} y - 1) d x + e^{x^{2}} d y

乘开

2 x d x (y e^{x^{2}} - 1) : 2 e^{x^{2}} x y d x - 2 x d x

= 2 e^{x^{2}} x y d x - 2 x d x + e^{x^{2}} d y

e x p an d \frac{2 π ( 2 2 - 2 )}{3}

e x p an d (c + 1) t e^{b t} sin (a t)

e x p an d (\frac{1}{x - 3}) + (\frac{1}{x ( x - 3 )})

e x p an d \frac{( x - 8 ) ( x + 6 ) ( x + 7 )}{4 x ( x - 4 ) ^{2}}

e x p an d \frac{( 3 n + 1 ) ( 3 n + 2 )}{( 3 n + 4 ) ( 3 n + 5 )}