8.5.34 problem 34

Internal problem ID [762]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 34
Date solved : Monday, January 27, 2025 at 03:04:03 AM
CAS classification : [_exact, _rational]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 117

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

\begin{align*} y &= -\frac {\sqrt {-2 x^{2}-2 \sqrt {x^{4}-4 x^{3}-4 c_1}}}{2} \\ y &= \frac {\sqrt {-2 x^{2}-2 \sqrt {x^{4}-4 x^{3}-4 c_1}}}{2} \\ y &= -\frac {\sqrt {-2 x^{2}+2 \sqrt {x^{4}-4 x^{3}-4 c_1}}}{2} \\ y &= \frac {\sqrt {-2 x^{2}+2 \sqrt {x^{4}-4 x^{3}-4 c_1}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.977 (sec). Leaf size: 155

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