Internal problem ID [15019]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 5. Homogeneous equations. Exercises page 44
Problem number: 112.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {3 y+\left (3 x +2 y-5\right ) y^{\prime }=-2 x +5} \]
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 33
dsolve((2*x+3*y(x)-5)+(3*x+2*y(x)-5)*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \frac {-\sqrt {5 \left (-1+x \right )^{2} c_{1}^{2}+4}+\left (-3 x +5\right ) c_{1}}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 65
DSolve[(2*x+3*y[x]-5)+(3*x+2*y[x]-5)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-\sqrt {5 x^2-10 x+25+4 c_1}-3 x+5\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5 x^2-10 x+25+4 c_1}-3 x+5\right ) \\ \end{align*}