58.2.10 problem 11

Internal problem ID [9133]
Book : Second order enumerated odes
Section : section 2
Problem number : 11
Date solved : Monday, January 27, 2025 at 05:48:37 PM
CAS classification : [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+{y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 14

dsolve(diff(y(x),x$2)+sin(x)*diff(y(x),x)+(diff(y(x),x))^2=0,y(x), singsol=all)
 

\[ y = \ln \left (c_{1} \left (\int {\mathrm e}^{\cos \left (x \right )}d x \right )+c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 3.314 (sec). Leaf size: 63

DSolve[D[y[x],{x,2}]+Sin[x]*D[y[x],x]+(D[y[x],x])^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\frac {\exp \left (\int _1^{K[3]}-\sin (K[1])dK[1]\right )}{c_1-\int _1^{K[3]}-\exp \left (\int _1^{K[2]}-\sin (K[1])dK[1]\right )dK[2]}dK[3]+c_2 \]