57.1.64 problem 64

Internal problem ID [9048]
Book : First order enumerated odes
Section : section 1
Problem number : 64
Date solved : Monday, January 27, 2025 at 05:31:03 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 33

dsolve(diff(y(x),x)=(Pi+x+7*y(x))^(7/2),y(x), singsol=all)
 

\[ y = -\frac {x}{7}+\operatorname {RootOf}\left (-x +7 \left (\int _{}^{\textit {\_Z}}\frac {1}{1+7 \left (\pi +7 \textit {\_a} \right )^{{7}/{2}}}d \textit {\_a} \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.532 (sec). Leaf size: 43

DSolve[D[y[x],x]==(Pi+x+7*y[x])^(7/2),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-(7 y(x)+x+\pi ) \left (\operatorname {Hypergeometric2F1}\left (\frac {2}{7},1,\frac {9}{7},-7 (x+7 y(x)+\pi )^{7/2}\right )-1\right )-7 y(x)=c_1,y(x)\right ] \]