29.37.4 problem 1117

Internal problem ID [5662]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1117
Date solved : Monday, January 27, 2025 at 01:02:14 PM
CAS classification : [_separable]

\begin{align*} 2 \left (y+1\right )^{{3}/{2}}+3 x y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 31

dsolve(2*(1+y(x))^(3/2)+3*x*diff(y(x),x)-3*y(x) = 0,y(x), singsol=all)
 

\[ \ln \left (x \right )+3 \left (\int _{}^{y \left (x \right )}\frac {1}{\left (2 \textit {\_a} +2\right ) \sqrt {\textit {\_a} +1}-3 \textit {\_a}}d \textit {\_a} \right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 55

DSolve[2 (1+y[x])^(3/2) + 3 x D[y[x],x]-3 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{3} \text {RootSum}\left [2 \text {$\#$1}^3-3 \text {$\#$1}^2+3\&,\frac {\log \left (\sqrt {y(x)+1}-\text {$\#$1}\right )}{\text {$\#$1}-1}\&\right ]=-\frac {\log (x)}{3}+c_1,y(x)\right ] \]