(1-x^2)y^'-x^2y=(1+x)sqrt(1-x^2)

解答

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

y = \frac{x + 1 \cdot \int \frac{e ^{x + c_{1}} x - 1 1 + x}{1 - x ^{2}} d x}{e ^{x + c_{1}} x - 1}

求解步骤

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

求解线性方程:

y = \frac{x + 1 \cdot \int \frac{e ^{x + c_{1}} x - 1 1 + x}{1 - x ^{2}} d x}{e ^{x + c_{1}} x - 1}

y = \frac{x + 1 \cdot \int \frac{e ^{x + c_{1}} x - 1 1 + x}{1 - x ^{2}} d x}{e ^{x + c_{1}} x - 1}

\int (x^{3} + x) d x

\frac{d}{d x} (arcsin (2 x))

\frac{\partial}{\partial x} (y ln (x))

\int 12 t^{3} d t

\frac{\partial}{\partial x} (x^{2} y + x y^{2} + 20)