2.791   ODE No. 791

$$y^{\prime }(x)=\frac{\text{sech}\left(\frac{1}{x-1}\right)(x^5+x^4-2x^{3}y(x)-2x^{2}y(x)+2x^2\cosh \left(\frac{1}{x-1}\right)+xy(x{)}^2+y(x{)}^2-x-2x\cosh \left(\frac{1}{x-1}\right)-1)}{x-1}$$

✓ Mathematica : cpu = 5.5567 (sec), leaf count = 110

DSolve[Derivative[1][y][x] == (Sech[(-1 + x)^(-1)]*(-1 - x + x^4 + x^5 - 2*x*Cosh[(-1 + x)^(-1)] + 2*x^2*Cosh[(-1 + x)^(-1)] - 2*x^2*y[x] - 2*x^3*y[x] + y[x]^2 + x*y[x]^2))/(-1 + x),y[x],x]
 

$$\left\{\{y(x)\to \frac{\exp ({\int }_1^x\frac{2(K[5]+1)\text{sech}\left(\frac{1}{K[5]-1}\right)}{K[5]-1}dK[5])}{-{\int }_1^x\frac{\exp ({\int }_1^{K[6]}\frac{2(K[5]+1)\text{sech}\left(\frac{1}{K[5]-1}\right)}{K[5]-1}dK[5])(K[6]+1)\text{sech}\left(\frac{1}{K[6]-1}\right)}{K[6]-1}dK[6]+c_1}+\frac{x^3+x^2}{x+1}+1\}\right\}$$

✓ Maple : cpu = 9.102 (sec), leaf count = 306

dsolve(diff(y(x),x) = (2*x^2*cosh(1/(x-1))-2*x*cosh(1/(x-1))-1+y(x)^2-2*x^2*y(x)+x^4-x+x*y(x)^2-2*x^3*y(x)+x^5)/(x-1)/cosh(1/(x-1)),y(x))
 

$$y\left(x\right)=\frac{(-x^2+1){\mathrm{e}}^{\frac{\int \frac{4{\mathrm{e}}^{\frac{1}{x-1}}(1+x)}{({\mathrm{e}}^{\frac{2}{x-1}}+1)(x-1)}dx}{{\mathrm{e}}^{\frac{2}{x-1}}+1}}{\mathrm{e}}^{\frac{(\int \frac{4{\mathrm{e}}^{\frac{1}{x-1}}(1+x)}{({\mathrm{e}}^{\frac{2}{x-1}}+1)(x-1)}dx){\mathrm{e}}^{\frac{2}{x-1}}}{{\mathrm{e}}^{\frac{2}{x-1}}+1}}+{\mathrm{e}}^{\frac{4c_1{\mathrm{e}}^{\frac{2}{x-1}}}{{\mathrm{e}}^{\frac{2}{x-1}}+1}}{\mathrm{e}}^{\frac{4c_1}{{\mathrm{e}}^{\frac{2}{x-1}}+1}}(x^2+1)}{{\mathrm{e}}^{\frac{4c_1{\mathrm{e}}^{\frac{2}{x-1}}}{{\mathrm{e}}^{\frac{2}{x-1}}+1}}{\mathrm{e}}^{\frac{4c_1}{{\mathrm{e}}^{\frac{2}{x-1}}+1}}-{\mathrm{e}}^{\frac{(\int \frac{4{\mathrm{e}}^{\frac{1}{x-1}}(1+x)}{({\mathrm{e}}^{\frac{2}{x-1}}+1)(x-1)}dx){\mathrm{e}}^{\frac{2}{x-1}}}{{\mathrm{e}}^{\frac{2}{x-1}}+1}}{\mathrm{e}}^{\frac{\int \frac{4{\mathrm{e}}^{\frac{1}{x-1}}(1+x)}{({\mathrm{e}}^{\frac{2}{x-1}}+1)(x-1)}dx}{{\mathrm{e}}^{\frac{2}{x-1}}+1}}}$$