15.8.7 problem 7

Internal problem ID [3010]
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
Date solved : Monday, January 27, 2025 at 07:07:43 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.011 (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: 1.875 (sec). Leaf size: 20

DSolve[(2*Exp[x[t]]-t^2)+(t*Exp[x[t]])*D[x[t],t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \log \left (\frac {t^2}{4}+\frac {c_1}{t^2}\right ) \]