15.8.49 problem 52

Internal problem ID [3052]
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
Date solved : Monday, January 27, 2025 at 07:12:41 AM
CAS classification : [_separable]

\begin{align*} 4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.025 (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: 0.171 (sec). Leaf size: 17

DSolve[{4*x*y[x]^2+(x^2+1)*D[y[x],x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2 \log \left (x^2+1\right )+1} \]