1/((x+7))(dx)/(dy)=e^{(3x-2y)}

解答

\frac{1}{( x + 7 )} \frac{d x}{d y} = e^{(3 x - 2 y)}

y = - \frac{ln ( - 2 \cdot \int \frac{1}{e ^{3 x} ( x + 7 )} d x )}{2}

求解步骤

\frac{1}{( x + 7 )} \frac{d}{d y} (x) = e^{(3 x - 2 y)}

求解可分离方程:

y = - \frac{ln ( - 2 \cdot \int \frac{1}{e ^{3 x} ( x + 7 )} d x )}{2}

y = - \frac{ln ( - 2 \cdot \int \frac{1}{e ^{3 x} ( x + 7 )} d x )}{2}

y^{^{'}} + \frac{10}{40 + 2 t} y = 0

(1 - t) \frac{d y}{d t} - y = 0

\frac{d x}{2 x} + \frac{d y}{2 y} = 0

\frac{d y}{d t} = - \frac{1}{50} (y - 25)

e^{y} y^{^{'}} = 4, y (0) = 2