Internal problem ID [9044]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 709.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (1+x \right ) y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 39
dsolve(diff(y(x),x) = (2*a*x+2*a+x^3*(-y(x)^2+4*a*x)^(1/2))/(x+1)/y(x),y(x), singsol=all)
\[ -\sqrt {4 a x -y \left (x \right )^{2}}-\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (x +1\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 3.881 (sec). Leaf size: 143
DSolve[y'[x] == (2*a + 2*a*x + x^3*Sqrt[4*a*x - y[x]^2])/((1 + x)*y[x]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{6} \sqrt {144 a x-\left (2 x^3-3 x^2+6 x+6 c_1\right ){}^2+12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)-36 \log ^2(x+1)} y(x)\to \frac {1}{6} \sqrt {144 a x-\left (2 x^3-3 x^2+6 x+6 c_1\right ){}^2+12 \left (2 x^3-3 x^2+6 x+6 c_1\right ) \log (x+1)-36 \log ^2(x+1)} \end{align*}