second order integrable as is

\[\begin {aligned} x^{\prime \prime }+3 x^{\prime }&=0 \end {aligned}\]

Entering second order integrable as is solverIntegrating both sides of the ODE w.r.t \(t\) gives

\begin{align*} \int \left (x^{\prime \prime }+3 x^{\prime }\right )d t &= 0 \\ x^{\prime }+3 x = c_1 \end{align*}

Which is now solved for \(x\). Entering ﬁrst order ode autonomous solverIntegrating gives

\begin{align*} \int \frac {1}{-3 x +c_1}d x &= dt\\ -\frac {\ln \left (-3 x +c_1 \right )}{3}&= t +c_2 \end{align*}

Solving for \(x\) from \(-\frac {\ln \left (-3 x+c_1 \right )}{3} = t +c_2\) gives

\begin{align*} x &= -\frac {{\mathrm e}^{-3 t -3 c_2}}{3}+\frac {c_1}{3} \\ \end{align*}