83.43.6 problem Ex 7 page 9

Internal problem ID [19514]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 7 page 9
Date solved : Tuesday, January 28, 2025 at 01:47:54 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 27

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

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

✓ Solution by Mathematica

Time used: 0.401 (sec). Leaf size: 57

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

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