# Calculator Riccati differential equation

## Riccati differential equation

y′(x) = f(x) ⋅ y2(x) + g(x) ⋅ y(x) + h(x)

with the initial values

y(x0) = y0

### Calculator for the initial value problem of the Riccati equation with the initial values x0, y0

The solution of the Riccati differential equation is solved numerically. The used method can be selected. Three Runge-Kutta methods are available: Heun, Euler and RK4. The initial value can be varied by dragging the red point on the solution curve. In the input fields for f, g and h, up to three parameters a, b and c are used which can be varied by means of the slider in the graphics.

Method:
Steps:
Scale screen:
Digits:
Grid points:
Scale grid:
Curve:
Grid:
f(x):
g(x):
h(x):

Initial values

x0=
y0=

Parameter value

a=
b=
c=

Axes ranges

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

Parameter ranges

a-min=
a-max=
b-min=
b-max=
c-min=
c-max=

f(x) =

 cl ok Pos1 End 7 8 9 / x 4 5 6 * π ( ) 1 2 3 - a b c 0 . + sin cos tan ex ln log10 asin acos atan x2 √x xy |x| sinh cosh

g(x) =

 cl ok Pos1 End 7 8 9 / x 4 5 6 * π ( ) 1 2 3 - a b c 0 . + sin cos tan ex ln log10 asin acos atan x2 √x xy |x| sinh cosh

h(x) =

 cl ok Pos1 End 7 8 9 / x 4 5 6 * π ( ) 1 2 3 - a b c 0 . + sin cos tan ex ln log10 asin acos atan x2 √x xy |x| sinh cosh

### Usable expressions in the definition of the functions f, g and h

Constants

NameDescription
LN2Natural logarithm of 2
LN10Natural logarithm of 10
LOG2EBase 2 logarithm of EULER
LOG10EBase 10 logarithm of EULER
PIRatio of the circumference of a circle to its diameter
SQRT1_2Square root of 1/2
SQRT2Square root of 2

Trigonometric Functions

FunctionDescription
sin(x)sine of x
cos(x)Cosine of x
tan(x)Tangent of x
asin(x)arcsine
acos(x)arccosine of x
atan(x)arctangent of x
atan2(y, x)Returns the arctangent of the quotient of its arguments.
cosh(x)Hyperbolic cosine of x
sinh(x)Hyperbolic sine of x

Logarithm and Exponential

FunctionDescription
pow(x, y)xy
sqrt(x)Square root of x
exp(x)ex
log(x), ln(x)Natural logarithm
log(x, b)Logarithm to base b
log2(x), lb(x)Logarithm to base 2
log10(x), ld(x)Logarithm to base 10

More functions

FunctionDescription
ceil(x)Get smallest integer n with n > x.
abs(x)Absolute value of x
max(a, b, c, ...)Maximum value of all given values.
min(a, b, c, ...)Minimum value of all given values.
random(max = 1)Generate a random number between 0 and max.
round(v)Returns the value of a number rounded to the nearest integer.
floor(x)Returns the biggest integer n with n < x.
factorial(n)Calculates n!
trunc(v, p = 0)Truncate v after the p-th decimal.
V(s)Returns the value of the given element, e.g. sliders and angles.

### Screenshot of the logistc growth graph

Print or save the image via right mouse click.

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