Internal problem ID [2062]
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: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {3 \,{\mathrm e}^{x} \tan \left (y\right )-\left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 144
dsolve(3*exp(x)*tan(y(x))=(1-exp(x))*sec(y(x))^2*diff(y(x),x),y(x), singsol=all)
\[ y = \frac {\arctan \left (\frac {2 c_{1} \left ({\mathrm e}^{3 x}-3 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{x}-1\right )}{{\mathrm e}^{6 x}-6 \,{\mathrm e}^{5 x}+15 \,{\mathrm e}^{4 x}-20 \,{\mathrm e}^{3 x}+15 \,{\mathrm e}^{2 x}+c_{1}^{2}-6 \,{\mathrm e}^{x}+1}, \frac {{\mathrm e}^{6 x}-6 \,{\mathrm e}^{5 x}+15 \,{\mathrm e}^{4 x}-20 \,{\mathrm e}^{3 x}+15 \,{\mathrm e}^{2 x}-c_{1}^{2}-6 \,{\mathrm e}^{x}+1}{{\mathrm e}^{6 x}-6 \,{\mathrm e}^{5 x}+15 \,{\mathrm e}^{4 x}-20 \,{\mathrm e}^{3 x}+15 \,{\mathrm e}^{2 x}+c_{1}^{2}-6 \,{\mathrm e}^{x}+1}\right )}{2} \]
✓ Solution by Mathematica
Time used: 1.19 (sec). Leaf size: 78
DSolve[3*Exp[x]*Tan[y[x]]==(1-Exp[x])*Sec[y[x]]^2*y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \arccos \left (-\tanh \left (-3 \log \left (2-2 e^x\right )+2 c_1\right )\right ) y(x)\to \frac {1}{2} \arccos \left (-\tanh \left (-3 \log \left (2-2 e^x\right )+2 c_1\right )\right ) y(x)\to 0 y(x)\to -\frac {\pi }{2} y(x)\to \frac {\pi }{2} \end{align*}