sqrt(x-1)(dy)/(dx)= x/y ,y=1,y>0,x=2

Lösung

x - 1 \frac{d y}{d x} = \frac{x}{y}, y = 1, y > 0, x = 2

y = 4 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + x - 1) + c_{1}, y = - 4 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + x - 1) + c_{1}

Schritte zur Lösung

x - 1 \frac{d y}{d x} = \frac{x}{y}

Solve separable ODE:

y = 4 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + x - 1) + c_{1}, y = - 4 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + x - 1) + c_{1}

y = 4 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + x - 1) + c_{1}, y = - 4 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + x - 1) + c_{1}

y^{^{'}} - \frac{y}{1 + e ^{x}} = 0

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

cos^{2} (x) (y^{^{'}}) = y^{2} + 1

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

y^{^{'}} - a^{2} 3 y = 0