(dy)/(dt)=t\sqrt[3]{y}

解答

\frac{d y}{d t} = t 3 y

y = \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}, y = - \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}

求解步骤

\frac{d y}{d t} = t 3 y

求解可分离方程:

y = \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}, y = - \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}

y = \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}, y = - \frac{t ^{6} + 8 c _{1}^{3} + 6 c _{1} t ^{4} + 12 c _{1}^{2} t ^{2}}{3 3}

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

\int_{0}^{π} (sin^{2} (x)) d x

\int (4 x + 1)^{2} e^{2 x} d x

\int cos (\frac{2}{3} x) d x

y^{^{''}} + 4 y^{^{'}} + 3 y = 20 t e^{5 t}