62.8.3 problem Ex 3

Internal problem ID [12831]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter 2, differential equations of the first order and the first degree. Article 15. Page 22
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:25:55 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 1.806 (sec). Leaf size: 47

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

\begin{align*} y &= -\frac {c_{1} \left (-c_{1} +\sqrt {4 x^{4}+c_{1}^{2}}\right )}{2 x} \\ y &= \frac {c_{1} \left (c_{1} +\sqrt {4 x^{4}+c_{1}^{2}}\right )}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.891 (sec). Leaf size: 76

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

\begin{align*} y(x)\to \frac {2 x^4}{-x+\frac {\sqrt {1+4 c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to -\frac {2 x^4}{x+\frac {\sqrt {1+4 c_1 x^4}}{\sqrt {\frac {1}{x^2}}}} \\ y(x)\to 0 \\ \end{align*}