56.1.2 problem 2

Internal problem ID [8714]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 2
Date solved : Monday, January 27, 2025 at 04:20:07 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

dsolve(diff(y(x),x) = x*(cos(y(x))+y(x)),y(x), singsol=all)
 

\[ \frac {x^{2}}{2}-\int _{}^{y}\frac {1}{\cos \left (\textit {\_a} \right )+\textit {\_a}}d \textit {\_a} +c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.626 (sec). Leaf size: 33

DSolve[D[y[x],x] == x*(Cos[y[x]]+y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{\cos (K[1])+K[1]}dK[1]\&\right ]\left [\frac {x^2}{2}+c_1\right ] \]