Internal problem ID [2081]
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: 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {4 y^{2} x +\left (x^{2}+1\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([4*x*y(x)^2+(x^2+1)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y = \frac {1}{1+2 \ln \left (x^{2}+1\right )} \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 17
DSolve[{4*x*y[x]^2+(x^2+1)*y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2 \log \left (x^2+1\right )+1} \]