60.2.272 problem 848

Internal problem ID [10859]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 848
Date solved : Tuesday, January 28, 2025 at 05:25:49 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(y)]`]]

\begin{align*} y^{\prime }&=\frac {\cosh \left (x \right )}{\sinh \left (x \right )}+\textit {\_F1} \left (y-\ln \left (\sinh \left (x \right )\right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 22

dsolve(diff(y(x),x) = 1/sinh(x)*cosh(x)+_F1(y(x)-ln(sinh(x))),y(x), singsol=all)
 

\[ y = \ln \left (\sinh \left (x \right )\right )+\operatorname {RootOf}\left (x -\int _{}^{\textit {\_Z}}\frac {1}{f_{1} \left (\textit {\_a} \right )}d \textit {\_a} +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.378 (sec). Leaf size: 148

DSolve[D[y[x],x] == Coth[x] + F1[-Log[Sinh[x]] + y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(x)}-\frac {\text {F1}(K[2]-\log (\sinh (x))) \int _1^x\left (\frac {(\coth (K[1])+\text {F1}(K[2]-\log (\sinh (K[1])))) \text {F1}''(K[2]-\log (\sinh (K[1])))}{\text {F1}(K[2]-\log (\sinh (K[1])))^2}-\frac {\text {F1}''(K[2]-\log (\sinh (K[1])))}{\text {F1}(K[2]-\log (\sinh (K[1])))}\right )dK[1]-1}{\text {F1}(K[2]-\log (\sinh (x)))}dK[2]+\int _1^x-\frac {\coth (K[1])+\text {F1}(y(x)-\log (\sinh (K[1])))}{\text {F1}(y(x)-\log (\sinh (K[1])))}dK[1]=c_1,y(x)\right ] \]