Internal problem ID [2077]
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: 48.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Bernoulli]
\[ \boxed {x^{\prime }-x-x^{2} {\mathrm e}^{\theta }=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 16
dsolve([diff(x(theta),theta)=x(theta)+x(theta)^2*exp(theta),x(0) = 2],x(theta), singsol=all)
\[ x \left (\theta \right ) = -\frac {2 \,{\mathrm e}^{\theta }}{{\mathrm e}^{2 \theta }-2} \]
✓ Solution by Mathematica
Time used: 0.217 (sec). Leaf size: 19
DSolve[{x'[\[Theta]]==x[\[Theta]]+x[\[Theta]]^2*Exp[\[Theta]],{x[0]==2}},x[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\[ x(\theta )\to -\frac {2 e^{\theta }}{e^{2 \theta }-2} \]