Internal problem ID [7046]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x \left (\cos \left (y\right )+y\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(diff(y(x),x) = x*(cos(y(x))+y(x)),y(x), singsol=all)
\[ \frac {x^{2}}{2}-\left (\int _{}^{y \left (x \right )}\frac {1}{\cos \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} \right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.71 (sec). Leaf size: 33
DSolve[y'[x] == x*(Cos[y[x]]+y[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\cos (K[1])+K[1]}dK[1]\&\right ]\left [\frac {x^2}{2}+c_1\right ] \]