Internal problem ID [15127]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 11. Singular solutions of differential equations. Exercises page 92
Problem number: 265.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {\left (y^{\prime } x +y\right )^{2}+3 x^{5} \left (y^{\prime } x -2 y\right )=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 65
dsolve((x*diff(y(x),x)+y(x))^2+3*x^5*(x*diff(y(x),x)-2*y(x))=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {x^{5}}{4} \\ y \left (x \right ) &= \frac {c_{1} \left (x^{3}+c_{1} \right )}{x} \\ y \left (x \right ) &= \frac {c_{1} \left (-x^{3}+c_{1} \right )}{x} \\ y \left (x \right ) &= \frac {c_{1} \left (-x^{3}+c_{1} \right )}{x} \\ y \left (x \right ) &= \frac {c_{1} \left (x^{3}+c_{1} \right )}{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.645 (sec). Leaf size: 94
DSolve[(x*y'[x]+y[x])^2+3*x^5*(x*y'[x]-2*y[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i (\cosh (3 c_1)+\sinh (3 c_1)) \left (x^3-i \cosh (3 c_1)-i \sinh (3 c_1)\right )}{x} \\ y(x)\to \frac {i (\cosh (3 c_1)+\sinh (3 c_1)) \left (x^3+i \cosh (3 c_1)+i \sinh (3 c_1)\right )}{x} \\ y(x)\to 0 \\ \end{align*}