75.11.6 problem 265

Internal problem ID [16857]
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
Date solved : Tuesday, January 28, 2025 at 09:35:20 AM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} \left (x y^{\prime }+y\right )^{2}+3 x^{5} \left (x y^{\prime }-2 y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.089 (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 &= -\frac {x^{5}}{4} \\ y &= \frac {c_{1} \left (x^{3}+c_{1} \right )}{x} \\ y &= \frac {c_{1} \left (-x^{3}+c_{1} \right )}{x} \\ y &= \frac {c_{1} \left (-x^{3}+c_{1} \right )}{x} \\ y &= \frac {c_{1} \left (x^{3}+c_{1} \right )}{x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 1.893 (sec). Leaf size: 94

DSolve[(x*D[y[x],x]+y[x])^2+3*x^5*(x*D[y[x],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*}