y^5(dy)/(dx)=5x^3y^6-15x^3

解答

y^{5} \frac{d y}{d x} = 5 x^{3} y^{6} - 15 x^{3}

y = 6 e^{c_{1} + \frac{15 x ^{4}}{2}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{15 x ^{4}}{2}} + 33 \cdot 3^{\frac{2}{3}}

求解步骤

y^{5} \frac{d y}{d x} = 5 x^{3} y^{6} - 15 x^{3}

求解可分离方程:

y = 6 e^{c_{1} + \frac{15 x ^{4}}{2}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{15 x ^{4}}{2}} + 33 \cdot 3^{\frac{2}{3}}

y = 6 e^{c_{1} + \frac{15 x ^{4}}{2}} + 33 \cdot 3^{\frac{2}{3}}, y = - 6 e^{c_{1} + \frac{15 x ^{4}}{2}} + 33 \cdot 3^{\frac{2}{3}}

\frac{( 9 + x ^{2} ) d y}{d x} - x y = x

y^{^{'}} = \frac{5 x ^{2} - 1}{5 + 6 y}

2 x y^{^{'}} + x^{2} y = 0

y^{^{'}} = \frac{x + x y ^{2}}{4 x}

\frac{d y}{d x} = \frac{sin ( 5 x )}{y}