54.2.417 problem 996

Internal problem ID [12291]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 996
Date solved : Wednesday, October 01, 2025 at 01:28:39 AM
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*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 15

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

\[ y = \operatorname {Si}\left (x \right )+\frac {1}{c_1 -\ln \left (x \right )} \]

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 23

ode=D[y[x],x] == (Sin[x] + (-SinIntegral[x] + y[x])^2)/x; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.839 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - ((y(x) - Si(x))**2 + sin(x))/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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