f^'(x)f(x)=x^2+10x-5

Lösung

f^{^{'}} (x) f (x) = x^{2} + 10 x - 5

f (x) = \frac{2 x ^{3}}{3} + 10 x^{2} - 10 x + c_{1}, f (x) = - \frac{2 x ^{3}}{3} + 10 x^{2} - 10 x + c_{1}

Schritte zur Lösung

f^{'} (x) f (x) = x^{2} + 10 x - 5

Solve separable ODE:

f (x) = \frac{2 x ^{3}}{3} + 10 x^{2} - 10 x + c_{1}, f (x) = - \frac{2 x ^{3}}{3} + 10 x^{2} - 10 x + c_{1}

f (x) = \frac{2 x ^{3}}{3} + 10 x^{2} - 10 x + c_{1}, f (x) = - \frac{2 x ^{3}}{3} + 10 x^{2} - 10 x + c_{1}

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

\frac{d y}{d x} + 2 x y = 25 x

x y^{^{'}} + 4 y + 8 = 0

\frac{d y}{d x} = - 3 x^{2} y

\frac{d y}{d x} y = x e^{- 4 x}