60.1.217 problem 222

Internal problem ID [10231]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 222
Date solved : Wednesday, March 05, 2025 at 08:44:58 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2 y+x +7\right ) y^{\prime }-y+2 x +4&=0 \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 32

ode:=(2*y(x)+x+7)*diff(y(x),x)-y(x)+2*x+4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -2+\tan \left (\operatorname {RootOf}\left (\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )-\textit {\_Z} +2 \ln \left (x +3\right )+2 c_{1} \right )\right ) \left (-x -3\right ) \]

✓ Mathematica. Time used: 0.06 (sec). Leaf size: 65

ode=(2*y[x]+x+7)*D[y[x],x]-y[x]+2*x+4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 \arctan \left (\frac {y(x)-2 (x+2)}{2 y(x)+x+7}\right )+2 \log \left (\frac {4 \left (x^2+y(x)^2+4 y(x)+6 x+13\right )}{5 (x+3)^2}\right )+4 \log (x+3)+5 c_1=0,y(x)\right ] \]

✓ Sympy. Time used: 1.993 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (x + 2*y(x) + 7)*Derivative(y(x), x) - y(x) + 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x + 3 \right )} = C_{1} - \log {\left (\sqrt {1 + \frac {\left (y{\left (x \right )} + 2\right )^{2}}{\left (x + 3\right )^{2}}} \right )} - \frac {\operatorname {atan}{\left (\frac {y{\left (x \right )} + 2}{x + 3} \right )}}{2} \]