75.5.7 problem 106

Internal problem ID [16743]
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 : 106
Date solved : Tuesday, January 28, 2025 at 09:20:39 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x -3 y+\left (2 y-3 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.162 (sec). Leaf size: 51

dsolve((4*x-3*y(x))+(2*y(x)-3*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {3 c_{1} x -\sqrt {c_{1}^{2} x^{2}+4}}{2 c_{1}} \\ y &= \frac {3 c_{1} x +\sqrt {c_{1}^{2} x^{2}+4}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.414 (sec). Leaf size: 95

DSolve[(4*x-3*y[x])+(2*y[x]-3*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (3 x-\sqrt {x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (3 x+\sqrt {x^2+4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (3 x-\sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {x^2}+3 x\right ) \\ \end{align*}