Internal problem ID [8576]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 996.
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-\sinIntegral \relax (x )\right )^{2}+\sin \relax (x )}{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 15
dsolve(diff(y(x),x) = ((y(x)-Si(x))^2+sin(x))/x,y(x), singsol=all)
\[ y \relax (x ) = \sinIntegral \relax (x )+\frac {1}{c_{1}-\ln \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.198 (sec). Leaf size: 23
DSolve[y'[x] == (Sin[x] + (-SinIntegral[x] + y[x])^2)/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {Si}(x)+\frac {1}{-\log (x)+c_1} \\ y(x)\to \text {Si}(x) \\ \end{align*}