Internal
problem
ID
[8102]
Book
:
Second
order
enumerated
odes
Section
:
section
2
Problem
number
:
14
Date
solved
:
Tuesday, October 22, 2024 at 03:00:21 PM
CAS
classification
:
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\begin{align*} 10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} {y^{\prime }}^{2}}{\sin \left (y\right )}&=0 \end{align*}
2.13.3 Maple dsolve solution
Solving time : 0.006 (sec)
Leaf size : 38
dsolve(10*diff(diff(y(x),x),x)+(exp(x)+3*x)*diff(y(x),x)+3/sin(y(x))*exp(y(x))*diff(y(x),x)^2 = 0,
y(x),singsol=all)
\[
\int _{}^{y}{\mathrm e}^{\frac {3 \left (\int {\mathrm e}^{\textit {\_b}} \csc \left (\textit {\_b} \right )d \textit {\_b} \right )}{10}}d \textit {\_b} -c_1 \left (\int {\mathrm e}^{-\frac {3 x^{2}}{20}-\frac {{\mathrm e}^{x}}{10}}d x \right )-c_2 = 0
\]
2.13.4 Mathematica DSolve solution
Solving time : 0.265 (sec)
Leaf size : 90
DSolve[{10*D[y[x],{x,2}]+(Exp[x]+3*x)*D[y[x],x]+3/Sin[y[x]]*Exp[y[x]]*(D[y[x],x])^2==0,{}},
y[x],x,IncludeSingularSolutions->True]
\[
y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\exp \left (\left (-\frac {3}{10}-\frac {3 i}{10}\right ) e^{(1+i) K[1]} \operatorname {Hypergeometric2F1}\left (\frac {1}{2}-\frac {i}{2},1,\frac {3}{2}-\frac {i}{2},e^{2 i K[1]}\right )\right )dK[1]\&\right ]\left [\int _1^x-e^{\frac {1}{20} \left (-3 K[2]^2-2 e^{K[2]}\right )} c_1dK[2]+c_2\right ]
\]