(dy)/(dx)y=(2x+1)^3

Lösung

\frac{d y}{d x} y = (2 x + 1)^{3}

y = \frac{16 x ^{4} + 32 x ^{3} + 24 x ^{2} + 8 x + 1 + c _{1}}{2}, y = - \frac{16 x ^{4} + 32 x ^{3} + 24 x ^{2} + 8 x + 1 + c _{1}}{2}

Schritte zur Lösung

\frac{d y}{d x} y = (2 x + 1)^{3}

Solve separable ODE:

y = \frac{16 x ^{4} + 32 x ^{3} + 24 x ^{2} + 8 x + 1 + c _{1}}{2}, y = - \frac{16 x ^{4} + 32 x ^{3} + 24 x ^{2} + 8 x + 1 + c _{1}}{2}

y = \frac{16 x ^{4} + 32 x ^{3} + 24 x ^{2} + 8 x + 1 + c _{1}}{2}, y = - \frac{16 x ^{4} + 32 x ^{3} + 24 x ^{2} + 8 x + 1 + c _{1}}{2}

\frac{d}{d x} (y^{2}) = x + 1

\frac{d x}{d t} = 7 x t^{5}

\frac{d y}{d x} + (\frac{( 1 - y ^{2} )}{( 1 - x ^{2} )}) = 0

y y^{^{'}} - 2 e x = 0, y (0) = 3

x y^{^{'}} + y = \frac{1}{3}