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AI Math Handbook Calculator

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

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


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


Output:
$$pdsolve(\frac{dy}{dt} - \frac{d^{{2}}y}{dx^{{2}}}=2\ z - 2\ y,\frac{dz}{dt} - \frac{d^{{2}}z}{dx^{{2}}}=4\ z - 4\ y)== y=\frac{1}{8}\ (2\ (C_1\ cos(1.4142135623730951\ x)+exp(2\ (C_1+t))+C_2\ sin(1.4142135623730951\ x))-4\ (2\ C_1+C_2\ x))\ and\ z=\frac{1}{2}\ ((-2)\ C_1+C_1\ cos(1.4142135623730951\ x)+exp(2\ (C_1+t))+C_2\ sin(1.4142135623730951\ x)-C_2\ x)$$ Result: $$y=\frac{1}{8}\ (2\ (C_1\ cos(1.4142135623730951\ x)+exp(2\ (C_1+t))+C_2\ sin(1.4142135623730951\ x))-4\ (2\ C_1+C_2\ x))\ and\ z=\frac{1}{2}\ ((-2)\ C_1+C_1\ cos(1.4142135623730951\ x)+exp(2\ (C_1+t))+C_2\ sin(1.4142135623730951\ x)-C_2\ x)$$
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