e^{x+y}sin(x)dx+(2y+1)e^{-y^2}dy=0

解答

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

y = - \frac{1 + 1 - 4 ln ( - c _{1} + \frac{- e ^{x} c o s ( x ) + e ^{x} s i n ( x )}{2} )}{2}, y = - \frac{1 - 1 - 4 ln ( - c _{1} + \frac{- e ^{x} c o s ( x ) + e ^{x} s i n ( x )}{2} )}{2}

求解步骤

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

求解可分离方程:

y = - \frac{1 + 1 - 4 ln ( - c _{1} + \frac{- e ^{x} c o s ( x ) + e ^{x} s i n ( x )}{2} )}{2}, y = - \frac{1 - 1 - 4 ln ( - c _{1} + \frac{- e ^{x} c o s ( x ) + e ^{x} s i n ( x )}{2} )}{2}

y = - \frac{1 + 1 - 4 ln ( - c _{1} + \frac{- e ^{x} c o s ( x ) + e ^{x} s i n ( x )}{2} )}{2}, y = - \frac{1 - 1 - 4 ln ( - c _{1} + \frac{- e ^{x} c o s ( x ) + e ^{x} s i n ( x )}{2} )}{2}

\frac{d y}{d x} = \frac{4 x y}{( ln ( y ) ) ^{2}}

y^{^{'}} = - y + 7

\frac{d}{d x} (\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}}) = 1

y^{^{'}} = 4 x^{2} y

y^{^{'}} = \frac{( x - 2 ) ^{2}}{y}, y (3) = 1