Processing math: 100%

AI Math Handbook Calculator

$oo$

$alpha$

$beta$

$gamma$

$Gamma$

$delta$

$theta$

$sin^(-1)(x)$

$cos^(-1)(x)$

$tan^(-1)(x)$
sinh(x) cosh(x) tanh(x) coth(x)

$sinh^(-1)(x)$

$cosh^(-1)(x)$

$tanh^(-1)(x)$
f(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)

$zeta(x)$

$E _0.5 (x^0.5)$

$sum_(x=0)^5$ (x)

$int$

$int$ 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:

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

Output:
$pdsolve(\frac{dy}{dt} - \frac{dy}{dx} =2\ z - 2\ y,\frac{dz}{dt} - \frac{dz}{dx} =4\ z - 4\ y)== y=\frac{1}{8}\ ((-8)\ C_1+2\ (C_1\ exp(2\ t)+C_1\ exp((-2.0)\ x)))\ and\ z=\frac{1}{2}\ ((-2)\ C_1+C_1\ exp(2\ t)+C_1\ exp((-2.0)\ x))$

Result:

$y=\frac{1}{8}\ ((-8)\ C_1+2\ (C_1\ exp(2\ t)+C_1\ exp((-2.0)\ x)))\ and\ z=\frac{1}{2}\ ((-2)\ C_1+C_1\ exp(2\ t)+C_1\ exp((-2.0)\ x))$

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