y^'=(y-1)^2-0.01

Lösung

y^{^{'}} = (y - 1)^{2} - 0.01

y = - \frac{0.9 e ^{\frac{t + c _{1}}{5}}}{1 - e ^{\frac{c _{1} + t}{5}}} + \frac{1.1}{1 - e ^{\frac{c _{1} + t}{5}}}

Schritte zur Lösung

y^{'} (t) = (y - 1)^{2} - 0.01

Solve separable ODE:

y = - \frac{0.9 e ^{\frac{t + c _{1}}{5}}}{1 - e ^{\frac{c _{1} + t}{5}}} + \frac{1.1}{1 - e ^{\frac{c _{1} + t}{5}}}

y = - \frac{0.9 e ^{\frac{t + c _{1}}{5}}}{1 - e ^{\frac{c _{1} + t}{5}}} + \frac{1.1}{1 - e ^{\frac{c _{1} + t}{5}}}

y^{^{'}} + \frac{1}{1 - x ^{2}} y = \frac{3}{1 - x ^{2}}

y^{^{'}} - 3 y = - 4

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

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

(2 t - 1) y^{^{'}} - 4 y = 0