Internal problem ID [2039]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {2 \,{\mathrm e}^{x}+t \,{\mathrm e}^{x} x^{\prime }=t^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve((2*exp(x(t))-t^2)+(t*exp(x(t)))*diff(x(t),t)=0,x(t), singsol=all)
\[ x \left (t \right ) = -2 \ln \left (2\right )+\ln \left (\frac {t^{4}+c_{1}}{t^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 1.926 (sec). Leaf size: 20
DSolve[(2*Exp[x[t]]-t^2)+(t*Exp[x[t]])*x'[t]==0,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \log \left (\frac {t^2}{4}+\frac {c_1}{t^2}\right ) \]