60.2.208 problem 784

Internal problem ID [10795]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 784
Date solved : Monday, January 27, 2025 at 09:46:21 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]

\begin{align*} y^{\prime }&=\frac {-\sinh \left (x \right )+x^{2} \ln \left (x \right )+2 y \ln \left (x \right ) x +\ln \left (x \right )+y^{2} \ln \left (x \right )}{\sinh \left (x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 22

dsolve(diff(y(x),x) = (-sinh(x)+x^2*ln(x)+2*y(x)*ln(x)*x+ln(x)+y(x)^2*ln(x))/sinh(x),y(x), singsol=all)
 

\[ y = -x -\tan \left (c_{1} -\int \ln \left (x \right ) \operatorname {csch}\left (x \right )d x \right ) \]

✓ Solution by Mathematica

Time used: 0.450 (sec). Leaf size: 27

DSolve[D[y[x],x] == Csch[x]*(Log[x] + x^2*Log[x] - Sinh[x] + 2*x*Log[x]*y[x] + Log[x]*y[x]^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x+\tan \left (\int _1^x\text {csch}(K[5]) \log (K[5])dK[5]+c_1\right ) \]