75.7.2 problem 176

Internal problem ID [16795]
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 : 176
Date solved : Tuesday, January 28, 2025 at 09:27:37 AM
CAS classification : [_exact, _rational]

\begin{align*} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.063 (sec). Leaf size: 125

dsolve((3*x^2+6*x*y(x)^2)+(6*x^2*y(x)+4*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\sqrt {-6 x^{2}-2 \sqrt {9 x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y &= \frac {\sqrt {-6 x^{2}-2 \sqrt {9 x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y &= -\frac {\sqrt {-6 x^{2}+2 \sqrt {9 x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ y &= \frac {\sqrt {-6 x^{2}+2 \sqrt {9 x^{4}-4 x^{3}-4 c_{1}}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.111 (sec). Leaf size: 163

DSolve[(3*x^2+6*x*y[x]^2)+(6*x^2*y[x]+4*y[x]^3)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {-3 x^2-\sqrt {9 x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-3 x^2-\sqrt {9 x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to -\frac {\sqrt {-3 x^2+\sqrt {9 x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ y(x)\to \frac {\sqrt {-3 x^2+\sqrt {9 x^4-4 x^3+4 c_1}}}{\sqrt {2}} \\ \end{align*}