Internal problem ID [6698]
Book: Second order enumerated odes
Section: section 2
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {10 y^{\prime \prime }+\left ({\mathrm e}^{x}+3 x \right ) y^{\prime }+\frac {3 \,{\mathrm e}^{y} \left (y^{\prime }\right )^{2}}{\sin \relax (y)}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(10*diff(y(x),x$2)+(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)
\[ \int _{}^{y \relax (x )}{\mathrm e}^{\int \frac {3 \,{\mathrm e}^{\textit {\_b}}}{10 \sin \left (\textit {\_b} \right )}d \textit {\_b}}d \textit {\_b} -c_{1} \left (\int {\mathrm e}^{-\frac {3 x^{2}}{20}-\frac {{\mathrm e}^{x}}{10}}d x \right )-c_{2} = 0 \]
✓ Solution by Mathematica
Time used: 0.244 (sec). Leaf size: 90
DSolve[10*y''[x]+(Exp[x]+3*x)*y'[x]+3/Sin[y[x]]*Exp[y[x]]*(y'[x])^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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[2]} \, _2F_1\left (\frac {1}{2}-\frac {i}{2},1;\frac {3}{2}-\frac {i}{2};e^{2 i K[2]}\right )\right )dK[2]\&\right ]\left [\int _1^x-e^{\frac {1}{20} \left (-3 K[3]^2-2 e^{K[3]}\right )} c_1dK[3]+c_2\right ] \\ \end{align*}