75.6.19 problem 152

Internal problem ID [16775]
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 : Tuesday, January 28, 2025 at 09:22:10 AM
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*}

✓ Solution by Maple

Time used: 0.061 (sec). Leaf size: 14

dsolve([2*x*diff(y(x),x)-y(x)=1-2/sqrt(x),y(infinity) = -1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 12

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

\[ y(x)\to \frac {1}{\sqrt {x}}-1 \]