x(dy)/(dx)=x^3+14x^3y

Lösung

x \frac{d y}{d x} = x^{3} + 14 x^{3} y

y = \frac{e ^{\frac{14 x ^{3} + c _{1}}{3}}}{14} - \frac{1}{14}

Schritte zur Lösung

x \frac{d y}{d x} = x^{3} + 14 x^{3} y

Solve separable ODE:

y = \frac{e ^{\frac{14 x ^{3} + c _{1}}{3}}}{14} - \frac{1}{14}

y = \frac{e ^{\frac{14 x ^{3} + c _{1}}{3}}}{14} - \frac{1}{14}

\int c x y + \frac{1}{4}

t an g e n t f (x) = \frac{x}{4 x - 7}, at x = 1

t an g e n t - 5 x^{2} + x - 2

\int_{0}^{9} \frac{1}{81 + x ^{2}} d x

y^{^{''}} + 4 y^{^{'}} + 5 y = - 20 e^{t}, y (0) = - 4, y^{^{'}} (0) = 1