y′(x) = f(x) ⋅ y(x) + g(x) ⋅ y^{n}(x)

with the initial values

y(x_{0}) = y_{0}

The solution of the Bernoulli 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 the functions f and g, up to three parameters a, b and c are used which can be varied by means of the slider in the graphics.

f(x) =

cl |
ok |
Pos1 |
End |
|||||

7 |
8 |
9 |
/ |
x |
||||

4 |
5 |
6 |
* |
π |
( |
) |
||

1 |
2 |
3 |
- |
a |
b |
c |
||

0 |
. |
+ |
sin |
cos |
tan |
|||

e |
ln |
log |
asin |
acos |
atan |
|||

x |
√x |
x |
|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 |
|||

e |
ln |
log |
asin |
acos |
atan |
|||

x |
√x |
x |
|x| |
sinh |
cosh |

**Constants**

Name | Description |
---|---|

LN2 | Natural logarithm of 2 |

LN10 | Natural logarithm of 10 |

LOG2E | Base 2 logarithm of EULER |

LOG10E | Base 10 logarithm of EULER |

PI | Ratio of the circumference of a circle to its diameter |

SQRT1_2 | Square root of 1/2 |

SQRT2 | Square root of 2 |

**Trigonometric Functions**

Function | Description |
---|---|

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**

Function | Description |
---|---|

pow(x, y) | x^{y} |

sqrt(x) | Square root of x |

exp(x) | e^{x} |

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**

Function | Description |
---|---|

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. |

Print or save the image via right mouse click.

Here is a list of of further useful sites:

Calculator:

ODE first order General first order ODE ODE second order ODE-System 2x2 ODE-System 3x3 Exponential growth Logistic growth Riccati equationCalculator for single ODEs:

y'+ay=b y'=fy+gy^n y'+2xy=xe^(-x^2) y'+xy=x y'+y=x y'=y^2 y'+y^2=1 y'=(Ay-a)(By-b)