60.2.295 problem 872

Internal problem ID [10882]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 872
Date solved : Monday, January 27, 2025 at 10:20:27 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 49

dsolve(diff(y(x),x) = 1/5*(-30*x^3*y(x)+12*x^6+70*x^(7/2)-30*x^3-25*y(x)*x^(1/2)+50*x-25*x^(1/2)-25)/(-5*y(x)+2*x^3+10*x^(1/2)-5)/x,y(x), singsol=all)
 

\begin{align*} y &= \frac {2 x^{3}}{5}+2 \sqrt {x}-\sqrt {2 \ln \left (x \right )+c_{1}}-1 \\ y &= \frac {2 x^{3}}{5}+\sqrt {2 \ln \left (x \right )+c_{1}}+2 \sqrt {x}-1 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.470 (sec). Leaf size: 92

DSolve[D[y[x],x] == (-5 - 5*Sqrt[x] + 10*x - 6*x^3 + 14*x^(7/2) + (12*x^6)/5 - 5*Sqrt[x]*y[x] - 6*x^3*y[x])/(x*(-5 + 10*Sqrt[x] + 2*x^3 - 5*y[x])),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\sqrt {-\frac {1}{x}} \sqrt {-x (2 \log (x)+1+c_1)}-1 \\ y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\left (-\frac {1}{x}\right )^{3/2} x \sqrt {-x (2 \log (x)+1+c_1)}-1 \\ \end{align*}