75.4.17 problem 62

Internal problem ID [16719]
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
Date solved : Tuesday, January 28, 2025 at 09:19:30 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&=a \left (1+y x \right ) \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.004 (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)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 10

DSolve[{y[x]+x*D[y[x],x]==a*(1+x*y[x]),{y[1/a]==-a}},y[x],x,IncludeSingularSolutions -> True]
 

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