60.1.341 problem 342

Internal problem ID [10355]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 342
Date solved : Monday, January 27, 2025 at 07:25:43 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x \left (3 \,{\mathrm e}^{y x}+2 \,{\mathrm e}^{-y x}\right ) \left (x y^{\prime }+y\right )+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 20

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)
 

\[ y = \frac {-\ln \left (5\right )+\ln \left (-\ln \left (x \right )+c_{1} \right )}{x} \]

✓ Solution by Mathematica

Time used: 60.433 (sec). Leaf size: 163

DSolve[1 + (2/E^(x*y[x]) + 3*E^(x*y[x]))*x*(y[x] + x*D[y[x],x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\text {arccosh}\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 {\text {arccosh}\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 {\text {arccosh}\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 {\text {arccosh}\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*}