60.2.421 problem 998

Internal problem ID [11008]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 998
Date solved : Monday, January 27, 2025 at 10:40:25 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 27

dsolve(diff(y(x),x) = ((y(x)-ln(x)-Ci(x))^2+cos(x))/x,y(x), singsol=all)
 

\[ y = \ln \left (x \right )+\operatorname {Ci}\left (x \right )+\frac {-c_{1} x^{2}+1}{c_{1} x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.512 (sec). Leaf size: 36

DSolve[D[y[x],x] == (Cos[x] + (-CosIntegral[x] - Log[x] + y[x])^2)/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \operatorname {CosIntegral}(x)-\frac {2 x^2}{x^2-2 c_1}+\log (x)+1 \\ y(x)\to \operatorname {CosIntegral}(x)+\log (x)+1 \\ \end{align*}