83.6.2 problem 2

Internal problem ID [19118]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (E) at page 19
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:58:24 PM
CAS classification : [_exact, _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 1+4 y x +2 y^{2}+\left (1+4 y x +2 x^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 69

dsolve((1+4*x*y(x)+2*y(x)^2)+(1+4*x*y(x)+2*x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= \frac {-2 x^{2}-1+\sqrt {4 x^{4}-8 c_{1} x -4 x^{2}+1}}{4 x} \\ y \left (x \right ) &= \frac {-2 x^{2}-1-\sqrt {4 x^{4}-8 c_{1} x -4 x^{2}+1}}{4 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.621 (sec). Leaf size: 79

DSolve[(1+4*x*y[x]+2*y[x]^2)+(1+4*x*y[x]+2*x^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {2 x^2+\sqrt {4 x^4-4 x^2+16 c_1 x+1}+1}{4 x} \\ y(x)\to \frac {-2 x^2+\sqrt {4 x^4-4 x^2+16 c_1 x+1}-1}{4 x} \\ \end{align*}