Internal problem ID [7922]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 342.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {x \left (3 \,{\mathrm e}^{y x}+2 \,{\mathrm e}^{-y x}\right ) \left (x y^{\prime }+y\right )+1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(x*(3*exp(x*y(x))+2*exp(-x*y(x)))*(x*diff(y(x),x)+y(x))+1 = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (-\frac {\ln \relax (x )}{5}+\frac {c_{1}}{5}\right )}{x} \]
✓ Solution by Mathematica
Time used: 60.703 (sec). Leaf size: 163
DSolve[1 + (2/E^(x*y[x]) + 3*E^(x*y[x]))*x*(y[x] + x*y'[x])==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\cosh ^{-1}\left (\frac {1}{24} \left (-5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x} \\ y(x)\to \frac {\cosh ^{-1}\left (\frac {1}{24} \left (-5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x} \\ y(x)\to -\frac {\cosh ^{-1}\left (\frac {1}{24} \left (5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x} \\ y(x)\to \frac {\cosh ^{-1}\left (\frac {1}{24} \left (5 \sqrt {24+\log ^2\left (\frac {c_1}{x}\right )}-\log \left (\frac {c_1}{x}\right )\right )\right )}{x} \\ \end{align*}