20.4.35 problem Problem 51

Internal problem ID [3670]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 51
Date solved : Monday, January 27, 2025 at 07:53:48 AM
CAS classification : [_rational, _Bernoulli]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 23

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

\[ y \left (x \right ) = -\frac {2}{\left (x^{2}+1\right ) \left (\ln \left (x^{2}+1\right )-2\right )} \]

✓ Solution by Mathematica

Time used: 0.225 (sec). Leaf size: 24

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

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