Internal problem ID [8578]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 998.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)]], _Riccati]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\left (y-\ln \relax (x )-\cosineIntegral \relax (x )\right )^{2}+\cos \relax (x )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 27
dsolve(diff(y(x),x) = ((y(x)-ln(x)-Ci(x))^2+cos(x))/x,y(x), singsol=all)
\[ y \relax (x ) = \ln \relax (x )+\cosineIntegral \relax (x )+\frac {-c_{1} x^{2}+1}{c_{1} x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.779 (sec). Leaf size: 36
DSolve[y'[x] == (Cos[x] + (-CosIntegral[x] - Log[x] + y[x])^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {CosIntegral}(x)-\frac {2 x^2}{x^2-2 c_1}+\log (x)+1 \\ y(x)\to \text {CosIntegral}(x)+\log (x)+1 \\ \end{align*}