June 13, 2021 Compiled on June 13, 2021 at 12:22 Noon

1 How to solve a ﬁrst order ODE?

2 How to solve a ﬁrst oder ODE with initial condition?

3 How to solve a second order ODE?

4 How to solve and ODE and convert the result to latex string?

5 How to solve a PDE in sympy?

6 How to check if something is derivative?

7 How to ﬁnd function name and its arguments in a proc?

2 How to solve a ﬁrst oder ODE with initial condition?

3 How to solve a second order ODE?

4 How to solve and ODE and convert the result to latex string?

5 How to solve a PDE in sympy?

6 How to check if something is derivative?

7 How to ﬁnd function name and its arguments in a proc?

Solve \( y'(x)=1+2 x\) for \(y(x)\)

Solve \( y'(x)=1+2 x\) for \(y(x)\) with \(y(0)=3\)

Solve \( 9 y{\relax (x )} + \frac {d^{2}}{d x^{2}} y{\relax (x )} = 0\)

gives

\[ y{\relax (x )} = C_{1} \sin {\left (3 x \right )} + C_{2} \cos {\left (3 x \right )} \]

Solve \( y'(x)=1+2 x\) for \(y(x)\) with \(y(0)=3\)

\[ y{\relax (x )} = x^{2} + x + 3 \]

PDE solving is still limited in sympy. Here is how to solve ﬁrst order pde

Solve \( u_t(x,t)=u_x(x,t)\)

\[ u{\left (x,t \right )} = F{\left (t + x \right )} \]

This also works, which seems to be the more prefered way

Suppose one passes \(y(x)\) to a function, and the function wants to ﬁnd the name of this function and its argument. Here is an example

This prints