75.6.33 problem 166

Internal problem ID [16789]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 166
Date solved : Tuesday, January 28, 2025 at 09:23:00 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }-\tan \left (y\right )&=\frac {{\mathrm e}^{x}}{\cos \left (y\right )} \end{align*}

✗ Solution by Maple

dsolve(diff(y(x),x)-tan(y(x))=exp(x)/cos(y(x)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 11.608 (sec). Leaf size: 14

DSolve[D[y[x],x]-Tan[y[x]]==Exp[x]/Cos[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arcsin \left (e^x (x+c_1)\right ) \]