57.1.64 problem 64
Internal
problem
ID
[9048]
Book
:
First
order
enumerated
odes
Section
:
section
1
Problem
number
:
64
Date
solved
:
Wednesday, March 05, 2025 at 07:18:07 AM
CAS
classification
:
[[_homogeneous, `class C`], _dAlembert]
\begin{align*} y^{\prime }&=\left (\pi +x +7 y\right )^{{7}/{2}} \end{align*}
✓ Maple. Time used: 0.039 (sec). Leaf size: 33
ode:=diff(y(x),x) = (Pi+x+7*y(x))^(7/2);
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {x}{7}+\operatorname {RootOf}\left (-x +7 \left (\int _{}^{\textit {\_Z}}\frac {1}{1+7 \left (\pi +7 \textit {\_a} \right )^{{7}/{2}}}d \textit {\_a} \right )+c_{1} \right )
\]
✓ Mathematica. Time used: 0.532 (sec). Leaf size: 43
ode=D[y[x],x]==(Pi+x+7*y[x])^(7/2);
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\[
\text {Solve}\left [-(7 y(x)+x+\pi ) \left (\operatorname {Hypergeometric2F1}\left (\frac {2}{7},1,\frac {9}{7},-7 (x+7 y(x)+\pi )^{7/2}\right )-1\right )-7 y(x)=c_1,y(x)\right ]
\]
✓ Sympy. Time used: 67.756 (sec). Leaf size: 400
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-(x + 7*y(x) + pi)**(7/2) + Derivative(y(x), x),0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
\[
y{\left (x \right )} = C_{1} + 7 x + 7 \pi ^{3} \int \limits ^{- C_{2} - \frac {x}{7}} \frac {\sqrt {\pi - 7 r}}{2401 r^{3} \sqrt {\pi - 7 r} - 1029 r^{2} \pi \sqrt {\pi - 7 r} + 147 r \pi ^{2} \sqrt {\pi - 7 r} - 7 \pi ^{3} \sqrt {\pi - 7 r} - 1}\, dr + 1029 \pi \int \limits ^{- C_{2} - \frac {x}{7}} \frac {r^{2} \sqrt {\pi - 7 r}}{2401 r^{3} \sqrt {\pi - 7 r} - 1029 r^{2} \pi \sqrt {\pi - 7 r} + 147 r \pi ^{2} \sqrt {\pi - 7 r} - 7 \pi ^{3} \sqrt {\pi - 7 r} - 1}\, dr - 2401 \int \limits ^{- C_{2} - \frac {x}{7}} \frac {r^{3} \sqrt {\pi - 7 r}}{2401 r^{3} \sqrt {\pi - 7 r} - 1029 r^{2} \pi \sqrt {\pi - 7 r} + 147 r \pi ^{2} \sqrt {\pi - 7 r} - 7 \pi ^{3} \sqrt {\pi - 7 r} - 1}\, dr - 147 \pi ^{2} \int \limits ^{- C_{2} - \frac {x}{7}} \frac {r \sqrt {\pi - 7 r}}{2401 r^{3} \sqrt {\pi - 7 r} - 1029 r^{2} \pi \sqrt {\pi - 7 r} + 147 r \pi ^{2} \sqrt {\pi - 7 r} - 7 \pi ^{3} \sqrt {\pi - 7 r} - 1}\, dr - 49 \int \limits ^{- C_{2} - \frac {x}{7}} \frac {1}{2401 r^{3} \sqrt {\pi - 7 r} - 1029 r^{2} \pi \sqrt {\pi - 7 r} + 147 r \pi ^{2} \sqrt {\pi - 7 r} - 7 \pi ^{3} \sqrt {\pi - 7 r} - 1}\, dr
\]