The general linear first order differential equation is given as follows:
y′ + f(x)⋅y = g(x)
with the initial values
y(x_{0}) = y_{0}
The solution of the 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 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) =
g(x) =
Constants
Name | Description |
---|---|
LN2 | Natural logarithm of 2 |
LN10 | Natural logarithm of 10 |
LOG2E | Base 2 logarithm of e |
LOG10E | Base 10 logarithm of e |
PI | Ratio of the circumference of a circle to its diameter |
SQRT1_2 | Quadratwurzel von 1/2 |
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(b, e) | Power e to the b |
sqrt(x) | Square root of x |
exp(x) | Power x to e |
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. |
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Here is a list of of further useful calculators:
Calculator:
ODE first order General first order ODE ODE second order ODE-System 2x2 ODE-System 3x3 Exponential growth Logistic growth Riccati equation Bernoulli 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)