29.21.18 problem 594

Internal problem ID [5188]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 21
Problem number : 594
Date solved : Monday, January 27, 2025 at 10:18:34 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

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

\[ \frac {x^{2}}{2}-\frac {y \left (x \right )^{2}}{2}-2 y \left (x \right )-4 \ln \left (y \left (x \right )-2\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.356 (sec). Leaf size: 43

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

\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {\text {$\#$1}^2}{2}+2 \text {$\#$1}+4 \log (\text {$\#$1}-2)-6\&\right ]\left [\frac {x^2}{2}+c_1\right ] \\ y(x)\to 2 \\ \end{align*}