Last Updated 10/28/2022

Sage Essentials
Section 8: Differential Equations

System of DE

The desolve_system()command.

Example 4

Solve the IVP $\{\begin{array}{c}{x}^{″}+10x-4y=0\\ -4x+y^{″}+4y=0\end{array}$ , $x\left(0\right)=0,x^{\prime }\left(0\right)=1$ , and $y\left(0\right)=0,y^{\prime }\left(0\right)=-1$ .

Suppose x and y are functions in t.

Encode the two DE as de1 and de2.

Solve the system with the desolve_system()command with the initial conditions encoded in the form of $\left[0,x\left(0\right),y\left(0\right),x^{\prime }\left(0\right),y^{\prime }\left(0\right)\right]$.

Try this!

Solve the IVP $\{\begin{array}{c}{x}^{\prime }=-x+y\\ y^{\prime }=2x\end{array}$, $x\left(0\right)=0$ , and $y\left(0\right)=1$.