# 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:
Grid points:
Steps:
Scale vectors=
Method:
Curve:
Grid:

Initial values

x0=
y0=

Parameter values

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 xa ^ asin acos atan x2 √x ax a/x a/(x+b) 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 xa ^ asin acos atan x2 √x ax a/x a/(x+b) sinh cosh

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

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(b, e)e to the b
sqrt(x)Square root of x
exp(x)EULER to the 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

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 Image

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