3(yx^2+y)y^'+sqrt(2+y^2)=0,y(1)=2

解答

3 (y x^{2} + y) y^{^{'}} + 2 + y^{2} = 0, y (1) = 2

y = \frac{16 2 arctan ^{2} ( x ) + 2 π ^{2} + 48 3 π - 8 2 π arctan ( x ) - 192 3 arctan ( x ) + 576 2}{12 4 2}

求解步骤

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

求解可分离方程:

y = \frac{16 2 arctan ^{2} ( x ) + 2 π ^{2} + 48 3 π - 8 2 π arctan ( x ) - 192 3 arctan ( x ) + 576 2}{12 4 2}

y = \frac{16 2 arctan ^{2} ( x ) + 2 π ^{2} + 48 3 π - 8 2 π arctan ( x ) - 192 3 arctan ( x ) + 576 2}{12 4 2}

\frac{d y}{d x} = \frac{3 x 1 + y ^{2}}{y}

\frac{d y}{d t} + 2 y = 7, y (0) = 1

y^{^{'}} = 15 x^{2} y + 25 y + 9 x^{2} + 15

y^{^{'}} = \frac{2 x y}{1 + x ^{2}}

y^{^{'}} = (y - 1) (x + 1)