y^'=e^{x^2}sqrt(y^2-81)

Lösung

y^{^{'}} = e^{x^{2}} y^{2} - 81

y = \frac{9}{2 e ^{\frac{π erfi ( x ) + 2 c _{1}}{2}}} + \frac{9 e ^{\frac{π erfi ( x ) + 2 c _{1}}{2}}}{2}

Schritte zur Lösung

y^{'} (x) = e^{x^{2}} y^{2} - 81

Solve separable ODE:

y = \frac{9}{2 e ^{\frac{π erfi ( x ) + 2 c _{1}}{2}}} + \frac{9 e ^{\frac{π erfi ( x ) + 2 c _{1}}{2}}}{2}

y = \frac{9}{2 e ^{\frac{π erfi ( x ) + 2 c _{1}}{2}}} + \frac{9 e ^{\frac{π erfi ( x ) + 2 c _{1}}{2}}}{2}

y y^{^{'}} + t = t y^{2}

(6 + x^{8}) \frac{d y}{d x} = (\frac{x}{y})^{7}

5 y^{^{'}} = y cos (5 x), y (0) = 1

y^{^{'}} x - y = 0

ln (y^{2}) \frac{d y}{d x} = x^{2} y, y (1) = e^{2}