29.11.13 problem 304

Internal problem ID [4904]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 11
Problem number : 304
Date solved : Monday, January 27, 2025 at 09:47:25 AM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

dsolve((-x^2+4)*diff(y(x),x)+4*y(x) = (2+x)*y(x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.242 (sec). Leaf size: 32

DSolve[(4-x^2)D[y[x],x]+4 y[x]==(2+x)y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2-x}{(x+2) (-\log (x+2)+c_1)} \\ y(x)\to 0 \\ \end{align*}