Phase Line Diagram • Shelvean Kapita

About

This tool plots phase lines for autonomous ODEs $ y' = f(y) $.

Equilibrium points are found by scanning the interval for sign changes in $ f(y) $, then refining each root using the bisection method. This is a robust technique that reliably locates all roots even for non-smooth or piecewise-defined functions.

y' = f(y) = -y*sin(y)

Enter ODE

\( y' = f(y) \)

\( y' =\)

y min

y max

Show graph of f(y)

Supported Functions

sqrt(y)	$$ \sqrt{y} $$
cbrt(y)	$$ \sqrt[3]{y} $$
abs(y)	$$ \|y\| $$
sin(y)	$$ \sin y $$
cos(y)	$$ \cos y $$
tan(y)	$$ \tan y $$
asin(y)	$$ \arcsin y $$
acos(y)	$$ \arccos y $$
atan(y)	$$ \arctan y $$
sinh(y)	$$ \sinh y $$
cosh(y)	$$ \cosh y $$
tanh(y)	$$ \tanh y $$
exp(y)	$$ e^{y} $$
log(y)	$$ \ln y $$
log10(y)	$$ \log_{10} y $$
pi	$$ \pi $$
e	$$ e $$
ceil(y)	$$ \lceil y \rceil $$
floor(y)	$$ \lfloor y \rfloor $$
round(y)	$$ \mathrm{round}(y) $$
max(a,b)	$$ \max(a,b) $$
min(a,b)	$$ \min(a,b) $$

Phase Line Diagram for Autonomous Differential Equations

Supported Functions