75.7.20 problem 195

Internal problem ID [16813]
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
Date solved : Tuesday, January 28, 2025 at 09:33:34 AM
CAS classification : [_rational]

\begin{align*} 2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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 &= \frac {x^{2}+c_{1} +\sqrt {x^{4}+2 c_{1} x^{2}+c_{1}^{2}-84 x}}{6 x} \\ y &= \frac {x^{2}+c_{1} -\sqrt {x^{4}+2 c_{1} x^{2}+c_{1}^{2}-84 x}}{6 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.395 (sec). Leaf size: 86

DSolve[( 2*x*y[x]^2-3*y[x]^3)+( 7-3*x*y[x]^2 )*D[y[x],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*}