x^2y^'=y^2-2

Lösung

x^{2} y^{^{'}} = y^{2} - 2

y = \frac{2 e ^{22 c_{1}}}{e ^{\frac{2 2}{x}} - e ^{22 c_{1}}} + \frac{2 e ^{\frac{2 2}{x}}}{e ^{\frac{2 2}{x}} - e ^{22 c_{1}}}

Schritte zur Lösung

x^{2} y^{'} (x) = y^{2} - 2

Solve Bernoulli ODE:

y = \frac{2 e ^{22 c_{1}}}{e ^{\frac{2 2}{x}} - e ^{22 c_{1}}} + \frac{2 e ^{\frac{2 2}{x}}}{e ^{\frac{2 2}{x}} - e ^{22 c_{1}}}

y = \frac{2 e ^{22 c_{1}}}{e ^{\frac{2 2}{x}} - e ^{22 c_{1}}} + \frac{2 e ^{\frac{2 2}{x}}}{e ^{\frac{2 2}{x}} - e ^{22 c_{1}}}

x^{^{'}} + sin (t) \cdot x - sin (t) = 0

x^{2} d x - (y + x^{3} y) d y = 0

\frac{d x}{d t} = (1 + t) (1 + x)

y^{^{'}} = 3 y, y (0) = 5

y^{^{'}} = 3 y, y (0) = 3