60.2.419 problem 996

Internal problem ID [11006]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 996
Date solved : Monday, January 27, 2025 at 10:40:15 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\frac {\left (y-\operatorname {Si}\left (x \right )\right )^{2}+\sin \left (x \right )}{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

dsolve(diff(y(x),x) = ((y(x)-Si(x))^2+sin(x))/x,y(x), singsol=all)
 

\[ y = \operatorname {Si}\left (x \right )+\frac {1}{-\ln \left (x \right )+c_{1}} \]

✓ Solution by Mathematica

Time used: 0.189 (sec). Leaf size: 23

DSolve[D[y[x],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*}