Internal problem ID [2063]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {\sec \left (y\right )^{2} y^{\prime }-\tan \left (y\right )=2 x \,{\mathrm e}^{x}} \]
✗ 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: 10.872 (sec). Leaf size: 64
DSolve[Sec[y[x]]^2*y'[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*}