83.3.5 problem 5

Internal problem ID [19061]
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 (B) at page 9
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 12:49:47 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 54

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

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

✓ Solution by Mathematica

Time used: 0.362 (sec). Leaf size: 129

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

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