75.10.4 problem 235

Internal problem ID [16851]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 9. The Riccati equation. Exercises page 75
Problem number : 235
Date solved : Tuesday, January 28, 2025 at 09:34:57 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Riccati]

\begin{align*} x^{2} y^{\prime }&=x^{2} y^{2}+y x +1 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

dsolve(x^2*diff(y(x),x)=x^2*y(x)^2+x*y(x)+1,y(x), singsol=all)
 

\[ y = \frac {-\ln \left (x \right )+c_{1} -1}{x \left (\ln \left (x \right )-c_{1} \right )} \]

✓ Solution by Mathematica

Time used: 0.169 (sec). Leaf size: 33

DSolve[x^2*D[y[x],x]==x^2*y[x]^2+x*y[x]+1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\log (x)+1+c_1}{x \log (x)+c_1 x} \\ y(x)\to -\frac {1}{x} \\ \end{align*}