38.2.46 problem 46

Internal problem ID [6475]
Book : Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY. 2001
Section : Program 24. First order differential equations. Further problems 24. page 1068
Problem number : 46
Date solved : Monday, January 27, 2025 at 02:07:11 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {c_1 \,x^{2}+c_1 -1} \\ y &= -\sqrt {c_1 \,x^{2}+c_1 -1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.530 (sec). Leaf size: 61

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

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