Consider the non-linear system,

$$\left( \begin{array}{ccc} x_{1}' \\ x_{2}' \end{array} \right) = \left( \begin{array}{ccc} -x_{1} \\ x_{2}+x_{1}^2 \end{array} \right) $$

Find the solution of the initial value problem..I couldn't integrate the the equation to find $x_{2}$,since it involves two dependent variables $x_{1}$ and ${x_{2}}$.

Can someone help me for the same..

Thanking in advance

  • $\begingroup$ You want the solution to an initial value problem, but I see no initial values...? $\endgroup$ – Semiclassical Nov 4 '14 at 16:30

Here's a hint:

$x_1$ is not coupled to $x_2$. From the equation for $x_1'$, it's not hard to find that \begin{equation} x_1(t) = e^{-t}x_1(0). \end{equation}

Can you substitute this into the equation for $x_2'$ and solve from there?

  • $\begingroup$ I tried in that way..I am not getting the answer.. $\endgroup$ – Pravisha John Nov 4 '14 at 16:26

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