60.2.262 problem 838

Internal problem ID [10849]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 838
Date solved : Monday, January 27, 2025 at 10:14:59 PM
CAS classification : [_rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 y \sqrt {x}+4 x^{6}+40 x^{{7}/{2}}+100 x}{25 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 42

dsolve(diff(y(x),x) = 1/25*(30*x^3+25*x^(1/2)+25*y(x)^2-20*x^3*y(x)-100*y(x)*x^(1/2)+4*x^6+40*x^(7/2)+100*x)/x,y(x), singsol=all)
 

\[ y = \frac {\left (10 c_{1} -10 \ln \left (x \right )\right ) \sqrt {x}+2 c_{1} x^{3}-2 x^{3} \ln \left (x \right )+5}{-5 \ln \left (x \right )+5 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.304 (sec). Leaf size: 48

DSolve[D[y[x],x] == (Sqrt[x] + 4*x + (6*x^3)/5 + (8*x^(7/2))/5 + (4*x^6)/25 - 4*Sqrt[x]*y[x] - (4*x^3*y[x])/5 + y[x]^2)/x,y[x],x,IncludeSingularSolutions -> True]
 

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