(dy)/(dx)+4y=3,y(0)=0

解答

\frac{d y}{d x} + 4 y = 3, y (0) = 0

y = - \frac{3 e ^{- 4 x}}{4} + \frac{3}{4}

求解步骤

\frac{d y}{d x} + 4 y = 3

求解可分离方程:

y = - \frac{3 e ^{- 4 x}}{4} + \frac{3}{4}

y = - \frac{3 e ^{- 4 x}}{4} + \frac{3}{4}

\frac{d y}{d x} = \frac{x ( y - 4 ) + y - 4}{x ( y - 6 ) - 3 ( y - 6 )}

\frac{d y}{d x} = y^{2} + 4 y + 5

\frac{d y}{y ^{2}} = \frac{d x}{- x ^{2} + 4}

x e^{x} d x - 3 y^{2} d y = 0

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