54.1.19 problem 19

Internal problem ID [11333]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 19
Date solved : Tuesday, September 30, 2025 at 07:43:14 PM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }-\left (y+x \right )^{2}&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 16

ode:=diff(y(x),x)-(x+y(x))^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -x -\tan \left (-x +c_1 \right ) \]

✓ Mathematica. Time used: 0.341 (sec). Leaf size: 14

ode=D[y[x],x] - (y[x] + x)^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -x+\tan (x+c_1) \end{align*}

✓ Sympy. Time used: 0.162 (sec). Leaf size: 34

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

\[ y{\left (x \right )} = \frac {- C_{1} x + i C_{1} + x e^{2 i x} + i e^{2 i x}}{C_{1} - e^{2 i x}} \]