Internal problem ID [15083]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 7, Total differential equations. The integrating factor. Exercises page
61
Problem number: 195.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {2 y^{2} x -3 y^{3}+\left (7-3 y^{2} x \right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 65
dsolve(( 2*x*y(x)^2-3*y(x)^3)+( 7-3*x*y(x)^2 )*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x^{2}+c_{1} +\sqrt {x^{4}+2 c_{1} x^{2}+c_{1}^{2}-84 x}}{6 x} \\ y \left (x \right ) &= \frac {x^{2}-\sqrt {x^{4}+2 c_{1} x^{2}+c_{1}^{2}-84 x}+c_{1}}{6 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.406 (sec). Leaf size: 86
DSolve[( 2*x*y[x]^2-3*y[x]^3)+( 7-3*x*y[x]^2 )*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x^2-\sqrt {x^4+2 c_1 x^2-84 x+c_1{}^2}+c_1}{6 x} \\ y(x)\to \frac {x^2+\sqrt {x^4+2 c_1 x^2-84 x+c_1{}^2}+c_1}{6 x} \\ y(x)\to 0 \\ \end{align*}