15.8.54 problem 57

Internal problem ID [3057]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 57
Date solved : Monday, January 27, 2025 at 07:18:39 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 17

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

\[ y = \frac {1}{\sqrt {2-\sqrt {x^{2}+1}}} \]

✓ Solution by Mathematica

Time used: 4.265 (sec). Leaf size: 32

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

\[ y(x)\to \frac {\sqrt {-\sqrt {x^2+1}-2}}{\sqrt {x^2-3}} \]