7.5.34 problem 34

Internal problem ID [138]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 34
Date solved : Friday, February 07, 2025 at 07:57:02 AM
CAS classification : [_exact, _rational]

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

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 117

dsolve((2*x*y(x)^2+3*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: 6.265 (sec). Leaf size: 155

DSolve[(2*x*y[x]^2+3*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*}