xy^{''}=y^'+(y^')^3

解答

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

y = - \frac{1 - e ^{2 c_{1}} x ^{2}}{e ^{c_{1}}} + c_{2}, y = \frac{1 - e ^{2 c_{1}} x ^{2}}{e ^{c_{1}}} + c_{2}

求解步骤

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

使用替代法求解:

y = - \frac{1 - e ^{2 c_{1}} x ^{2}}{e ^{c_{1}}} + c_{2}, y = \frac{1 - e ^{2 c_{1}} x ^{2}}{e ^{c_{1}}} + c_{2}

y = - \frac{1 - e ^{2 c_{1}} x ^{2}}{e ^{c_{1}}} + c_{2}, y = \frac{1 - e ^{2 c_{1}} x ^{2}}{e ^{c_{1}}} + c_{2}