15.8.31 problem 32

Internal problem ID [3034]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 32
Date solved : Monday, January 27, 2025 at 07:09:58 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} \sec \left (y\right )^{2} y^{\prime }&=\tan \left (y\right )+2 x \,{\mathrm e}^{x} \end{align*}

✗ Solution by Maple

dsolve(sec(y(x))^2*diff(y(x),x)=tan(y(x))+2*x*exp(x),y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 10.426 (sec). Leaf size: 64

DSolve[Sec[y[x]]^2*D[y[x],x]==Tan[y[x]]+2*x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \arctan \left (e^x \left (x^2+2 c_1\right )\right ) \\ y(x)\to -\frac {1}{2} \pi e^{-x} \sqrt {e^{2 x}} \\ y(x)\to \frac {1}{2} \pi e^{-x} \sqrt {e^{2 x}} \\ \end{align*}