60.2.210 problem 786

Internal problem ID [10797]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 786
Date solved : Monday, January 27, 2025 at 09:48:15 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {y \ln \left (x \right )+\cosh \left (x \right ) x a y^{2}+\cosh \left (x \right ) x^{3} b}{x \ln \left (x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 33

dsolve(diff(y(x),x) = (y(x)*ln(x)+cosh(x)*x*a*y(x)^2+cosh(x)*x^3*b)/x/ln(x),y(x), singsol=all)
 

\[ y = \frac {\tan \left (\sqrt {a b}\, \left (\int \frac {x \cosh \left (x \right )}{\ln \left (x \right )}d x +c_{1} \right )\right ) x \sqrt {a b}}{a} \]

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 47

DSolve[D[y[x],x] == (b*x^3*Cosh[x] + Log[x]*y[x] + a*x*Cosh[x]*y[x]^2)/(x*Log[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{a K[1]^2+b}dK[1]=\int _1^x\frac {\cosh (K[2]) K[2]}{\log (K[2])}dK[2]+c_1,y(x)\right ] \]