Internal problem ID [6322]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 32.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {2 t +3 x+\left (x+2\right ) x^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 15.578 (sec). Leaf size: 29
dsolve(2*t+3*x(t)+(x(t)+2)*diff(x(t),t)=0,x(t), singsol=all)
\[ x \relax (t ) = -2-\frac {4 \left (t -3\right ) c_{1}+1+\sqrt {4 \left (t -3\right ) c_{1}+1}}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 60.173 (sec). Leaf size: 365
DSolve[2*t+3*x[t]+(x[t]+2)*x'[t]==0,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -2+\frac {1}{\frac {1}{6-2 t}-\frac {1}{2} \sqrt {\frac {1}{(t-3)^2+e^{\frac {4 c_1}{9}} (t-3)^4}-\sqrt {-\frac {1}{2 (t-3)^4+e^{\frac {4 c_1}{9}} (t-3)^6+e^{-\frac {4 c_1}{9}} (t-3)^2}}}} \\ x(t)\to -2+\frac {2}{\frac {1}{3-t}+\sqrt {\frac {1}{(t-3)^2+e^{\frac {4 c_1}{9}} (t-3)^4}-\sqrt {-\frac {1}{2 (t-3)^4+e^{\frac {4 c_1}{9}} (t-3)^6+e^{-\frac {4 c_1}{9}} (t-3)^2}}}} \\ x(t)\to -2+\frac {1}{\frac {1}{6-2 t}-\frac {1}{2} \sqrt {\sqrt {-\frac {1}{2 (t-3)^4+e^{\frac {4 c_1}{9}} (t-3)^6+e^{-\frac {4 c_1}{9}} (t-3)^2}}+\frac {1}{(t-3)^2+e^{\frac {4 c_1}{9}} (t-3)^4}}} \\ x(t)\to -2+\frac {2}{\frac {1}{3-t}+\sqrt {\sqrt {-\frac {1}{2 (t-3)^4+e^{\frac {4 c_1}{9}} (t-3)^6+e^{-\frac {4 c_1}{9}} (t-3)^2}}+\frac {1}{(t-3)^2+e^{\frac {4 c_1}{9}} (t-3)^4}}} \\ \end{align*}