37.4 problem 1117

Internal problem ID [3810]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 37
Problem number: 1117.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {2 \left (1+y\right )^{\frac {3}{2}}+3 y^{\prime } x -3 y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 33

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

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

Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 55

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

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