The 4th small class discussion class on fundamentals of information and communication

mathmatic Solving ordinary differential equations

（1） Use DSolve function （ perhaps DSolveValue, In the same way ）

Such as y’[x] = 2xy[x], solve y[x]( general solution ）
DSolve[y’[x] == 2xy[x], y[x], x]

Find out the special solution ： Above is the general solution and below is the special solution

Multiple general solutions can also be solved ：

Use /. The assignment statement extracts each general solution ：

Draw an image ：

Solving differential equations ：

Special solution ：

have access to D[y[x],x] Instead of y’[x]：

（2） Use NDSolve, Numerical solution , Special solution （ Expressed numerically ）

adopt Plot You can see specific images ：

Partial differential equations

（1） Use DSolve

(2)
Wave equation ：

Heat conduction equation （ There is no solution here ）：

Add initial conditions to solve the wave equation ： Use here Derivative Indicates that a term after partial derivation is 0 The initial value of the

Solve the heat conduction equation after adding the initial conditions ：