# Calculator first order differential equation

## Bernoulli differential equation

The Bernoulli differential equation is a special form of the first order nonlinear differential equation and is:

y′(x) = f(x) ⋅ y(x) + g(x) ⋅ yn(x)

with the initial values

y(x0) = y0

where y is a sought function of x and f(x) and g(x) are continuous functions on an interval I and n is a real number not equal to one. The Bernoulli differential equation occurs frequently in physics and engineering, especially in fluid mechanics and aerodynamics.

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

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.

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Method:
Steps:
Exponent n =
Grid points:
Scale grid:
Curve:
Grid:
f(x):
g(x):

Axes ranges

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

Initial values

x0=
y0=

Parameter value

a=
b=
c=

Parameter ranges

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

f(x) =

g(x) =

cl
ok
Pos1
End
7
8
9
/
x
4
5
6
*
a
b
c
1
2
3
-
π
(
)
0
.
+
sin
cos
tan
ex
ln
xa
a/x
^
asin
acos
atan
x2
√x
ax
a/(x+b)
|x|
sinh
cosh
a⋅x+c / b⋅x+c
a+x / b+x
x2-a2/ x2+b2
a / x+b
1+√x / 1-√y
exsin(x)cos(x)
x+a
ea⋅x
a⋅x2+b⋅x+c
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
pow(a, b)Power ab
sqrt(x)Square root of x
exp(x)e-function
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 ...

### Screenshot of the graph

Print or save the image via right mouse click.

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