# Calculator Riccati Differential Equation

## Riccati differential equation y'+y^2=1

$y′(x)+y(x)2=1$

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:

$k=\frac{1}{2}\mathrm{ln}\frac{{e}^{2{x}_{0}}\left(1-{y}_{0}\right)}{{y}_{0}+1}={x}_{0}+\mathrm{ln}\frac{1-{y}_{0}}{{y}_{0}+1}$

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

Scale screen:
Number of digits =
Grid points:
Scale grid vectors=
Curve:
Grid:

Initial values

x0=
y0=

Axes ranges

x-min=
x-max=
y-min=
y-max=

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