Internal problem ID [14989]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 62.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } x +y-a \left (y x +1\right )=0} \] With initial conditions \begin {align*} \left [y \left (\frac {1}{a}\right ) = -a\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 9
dsolve([y(x)+x*diff(y(x),x)=a*(1+x*y(x)),y(1/a) = -a],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{x} \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 10
DSolve[{y[x]+x*y'[x]==a*(1+x*y[x]),{y[1/a]==-a}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{x} \]