Home | math | handbook | dictionary | function | eq. | graphics | coding | example | help | ? | 中文

AI Math Handbook Calculator

+ - * / ^ ! o `oo` `alpha` `beta` `gamma` `Gamma` `theta` `pi` and ( )
sin(x) cos(x) tan(x) cot(x) sec(x) csc(x) `sin^(-1)(x)` `cos^(-1)(x)` `tan^(-1)(x)`
sinh(x) cosh(x) tanh(x) coth(x) `sinh^(-1)(x)` `cosh^(-1)(x)` `tanh^(-1)(x)`
x `x^2` `sqrt(x)` `root3(x)` `e^-x` exp(x) ln(x) log(x) `log_10 (x)` |x| W(x) `((3),(x))`
x! x!! `Gamma(x)` `gamma(2,0,x)` `psi(x)` erf(x) `Phi(x)` Ei(x) li(x) si(x) `zeta(x)` `E _0.5 (x^0.5)`
f(x)= x; `sum_(x=0)^5`(x) `int`y(x) dx `int y(x) (dx)^0.5` `int_0^1` sin(x) dx `d/dx`y(x) `(d^(1) y)/dx^(1)` `y^((1))(x)` y' y''








Input:
pdsolve(ds(y,t)-ds(y,x)=2z-2y,ds(z,t)-ds(z,x)=4z-4y)

Write:
`pdsolve(ds(y,t)-ds(y,x)=2z-2y,ds(z,t)-ds(z,x)=4z-4y)`


Compute:
$$pdsolve(\frac{dy}{dt} -\frac{dy}{dx} =(-2)\ y+2\ z,\frac{dz}{dt} -\frac{dz}{dx} =(-4)\ y+4\ z)$$


Output:
$$pdsolve(\frac{dy}{dt} -\frac{dy}{dx} =(-2)\ y+2\ z,\frac{dz}{dt} -\frac{dz}{dx} =(-4)\ y+4\ z)== y=\frac{1}{8}\ ((-8)\ c_1+2\ (exp(c_1+2\ t)+exp(c_1-2.0\ x)))\ and\ z=\frac{1}{2}\ ((-2)\ c_1+exp(c_1+2\ t)+exp(c_1-2.0\ x))$$ Result: $$y=\frac{1}{8}\ ((-8)\ c_1+2\ (exp(c_1+2\ t)+exp(c_1-2.0\ x)))\ and\ z=\frac{1}{2}\ ((-2)\ c_1+exp(c_1+2\ t)+exp(c_1-2.0\ x))$$
zoom graph by mouse wheel.

Home | list | about | wiki | forum | contact | donate | index | ? | 中文