Internal problem ID [12437]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 23.
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: 0.031 (sec). Leaf size: 205
dsolve(3*exp(x)*tan(y(x))+(1-exp(x))*sec(y(x))^2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\arctan \left (-\frac {2 c_{1} \left ({\mathrm e}^{3 x}-3 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{x}-1\right )}{-c_{1}^{2} {\mathrm e}^{6 x}+6 c_{1}^{2} {\mathrm e}^{5 x}-15 c_{1}^{2} {\mathrm e}^{4 x}+20 c_{1}^{2} {\mathrm e}^{3 x}-15 c_{1}^{2} {\mathrm e}^{2 x}+6 c_{1}^{2} {\mathrm e}^{x}-c_{1}^{2}-1}, \frac {c_{1}^{2} {\mathrm e}^{6 x}-6 c_{1}^{2} {\mathrm e}^{5 x}+15 c_{1}^{2} {\mathrm e}^{4 x}-20 c_{1}^{2} {\mathrm e}^{3 x}+15 c_{1}^{2} {\mathrm e}^{2 x}-6 c_{1}^{2} {\mathrm e}^{x}+c_{1}^{2}-1}{-c_{1}^{2} {\mathrm e}^{6 x}+6 c_{1}^{2} {\mathrm e}^{5 x}-15 c_{1}^{2} {\mathrm e}^{4 x}+20 c_{1}^{2} {\mathrm e}^{3 x}-15 c_{1}^{2} {\mathrm e}^{2 x}+6 c_{1}^{2} {\mathrm e}^{x}-c_{1}^{2}-1}\right )}{2} \]
✓ Solution by Mathematica
Time used: 1.829 (sec). Leaf size: 74
DSolve[3*Exp[x]*Tan[y[x]]+(1-Exp[x])*Sec[y[x]]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2} \arccos \left (-\tanh \left (3 \log \left (e^x-1\right )+2 c_1\right )\right ) \\ y(x)\to \frac {1}{2} \arccos \left (-\tanh \left (3 \log \left (e^x-1\right )+2 c_1\right )\right ) \\ y(x)\to 0 \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}