(2y-2)(dy)/(dx)=3x^2+4x+2

Lösung

(2 y - 2) \frac{d y}{d x} = 3 x^{2} + 4 x + 2

y = 1 + x^{3} + 2 x^{2} + 2 x + c_{1} + 1, y = 1 - x^{3} + 2 x^{2} + 2 x + c_{1} + 1

Schritte zur Lösung

(2 y - 2) \frac{d y}{d x} = 3 x^{2} + 4 x + 2

Solve separable ODE:

y = 1 + x^{3} + 2 x^{2} + 2 x + c_{1} + 1, y = 1 - x^{3} + 2 x^{2} + 2 x + c_{1} + 1

y = 1 + x^{3} + 2 x^{2} + 2 x + c_{1} + 1, y = 1 - x^{3} + 2 x^{2} + 2 x + c_{1} + 1

\frac{\partial}{\partial x} (x y^{2} + x^{2} y)

t an g e n t y = \frac{x ^{2} - 1}{x ^{2} + x + 1}

\int \frac{x ^{2} + 2 x - 1}{x ( x + 2 ) ( 2 x - 1 )} d x

\frac{\partial}{\partial x} (- 4 cos (x))

x \to 1 lim (4 x - 5)