Internal problem ID [15045]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {2 y^{\prime } x -y=1-\frac {2}{\sqrt {x}}} \] With initial conditions \begin {align*} [y \left (\infty \right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([2*x*diff(y(x),x)-y(x)=1-2/sqrt(x),y(infinity) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sqrt {x}-1}{\sqrt {x}} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 12
DSolve[{2*x*y'[x]-y[x]==1-2/Sqrt[x],{y[Infinity]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{\sqrt {x}}-1 \]