Calculator Riccati Differential Equation

Riccati differential equation y'+y^2=1

$$y^{\prime }\left(x\right)+{y\left(x\right)}^2=1$$

The general solution of the first order differential equation is:

$y\left(x\right)=\frac{e^{2x}-e^{2k}}{e^{2k}+e^{2x}}$

with the constant k and the initial values x₀, y₀:

$k=\frac{1}{2}\ln \frac{e^{2x_0}\left(1-y_0\right)}{y_0+1}=x_0+\ln \frac{1-y_0}{y_0+1}$

Calculator for the initial value problem: y'+y^2=1 with the initial values x₀, y₀

⃢ 1:1 2:1 5:4 16:9 9:16

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