Calculator for ordinary first order differential equations

The general linear first order differential equation is given as follows:

y′ + f(x)⋅y = g(x)

with the initial values

y(x₀) = y₀

ODE Calculator with numerical solution and direction field

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.

Scale screen:

Scale vectors=

Grid points:

Steps:

Method:

Curve:

Grid:

f(x) =

g(x) =

Pos1

End

(

)

sin

cos

tan

e^x

x^a

a/x

asin

acos

atan

x²

√x

a^x

a/(x+b)

|x|

sinh

cosh

Usable expressions in the definition of the functions f and g

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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Calculator:

ODE first order General first order ODE ODE second order ODE-System 2x2 ODE-System 3x3 Exponential growth Logistic growth Riccati equation Bernoulli equation

Calculator 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)