Internal problem ID [6627]
Book: First order enumerated odes
Section: section 1
Problem number: 64.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime }-\left (\pi +x +7 y\right )^{\frac {7}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.041 (sec). Leaf size: 74
dsolve(diff(y(x),x)=(Pi+x+7*y(x))^(7/2),y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{7}+\RootOf \left (-x +7 \left (\int _{}^{\textit {\_Z}}\frac {1}{7 \pi ^{3} \sqrt {\pi +7 \textit {\_a}}+147 \pi ^{2} \textit {\_a} \sqrt {\pi +7 \textit {\_a}}+1029 \pi \,\textit {\_a}^{2} \sqrt {\pi +7 \textit {\_a}}+2401 \textit {\_a}^{3} \sqrt {\pi +7 \textit {\_a}}+1}d \textit {\_a} \right )+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 30.505 (sec). Leaf size: 43
DSolve[y'[x]==(Pi+x+7*y[x])^(7/2),y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-(7 y(x)+x+\pi ) \left (\, _2F_1\left (\frac {2}{7},1;\frac {9}{7};-7 (x+7 y(x)+\pi )^{7/2}\right )-1\right )-7 y(x)=c_1,y(x)\right ] \]