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Quiz-6 / Q6--T0501

« on: March 16, 2018, 07:19:49 PM »

For the given equation:$\\$
    a. Express the general solution of the given system of equations in terms of real-valued functions. $\\$
    b. Also draw a direction field, sketch a few of the trajectories, and describe the behaviour of solutions as $t \rightarrow \infty$.
$$\textbf{x}'=\begin{pmatrix}2&-5\\1&-2\end{pmatrix}\textbf{x}$$

2

Quiz-4 / Q4-T0501

« on: March 02, 2018, 04:56:49 PM »

Verify the given functions $y_1$ and $y_2$ satisfy the correspending homogeneous equation; then find a particular solution of the given nonhomogeneous equation.
\begin{align*}
&(1-t)y’’+ty’-y=2(t-1)^2e^{-t}, 0< t<1\\
 &y_1(t)=e^t, y_2(t)=t.
\end{align*}