29.37.30 problem 1153

Internal problem ID [5688]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1153
Date solved : Monday, January 27, 2025 at 01:07:11 PM
CAS classification : [_dAlembert]

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

✓ Solution by Maple

Time used: 0.137 (sec). Leaf size: 33

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

\begin{align*} y \left (x \right ) &= 0 \\ x -\int _{}^{y \left (x \right )}\frac {1}{\operatorname {RootOf}\left (\ln \left (\cos \left (\textit {\_Z} \right )\right )+\tan \left (\textit {\_Z} \right ) \textit {\_Z} -\textit {\_a} \right )}d \textit {\_a} -c_{1} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 29

DSolve[Log[Cos[D[y[x],x]]]+D[y[x],x]*Tan[D[y[x],x]]==y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}[\{x=\tan (K[1])+c_1,y(x)=K[1] \tan (K[1])+\log (\cos (K[1]))\},\{y(x),K[1]\}] \]