69.6.19 problem 152

Internal problem ID [18062]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 152
Date solved : Thursday, October 02, 2025 at 02:36:41 PM
CAS classification : [_linear]

\begin{align*} 2 x y^{\prime }-y&=1-\frac {2}{\sqrt {x}} \end{align*}

With initial conditions

\begin{align*} y \left (\infty \right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.050 (sec). Leaf size: 14

ode:=2*x*diff(y(x),x)-y(x) = 1-2/x^(1/2); 
ic:=[y(infinity) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {-1+\sqrt {x}}{\sqrt {x}} \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 12

ode=2*x*D[y[x],x]-y[x]==1-2/Sqrt[x]; 
ic={y[Infinity]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{\sqrt {x}}-1 \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x*Derivative(y(x), x) - y(x) - 1 + 2/sqrt(x),0) 
ics = {y(oo): -1} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions