75.5.13 problem 112

Internal problem ID [16749]
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
Date solved : Tuesday, January 28, 2025 at 09:21:02 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 1.759 (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)
 

\[ y = \frac {-\sqrt {5 \left (x -1\right )^{2} c_{1}^{2}+4}+\left (-3 x +5\right ) c_{1}}{2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.134 (sec). Leaf size: 65

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