Internal problem ID [9140]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 805.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-\frac {x y+y+\sqrt {x^{2}+y^{2}}\, x^{4}}{x \left (1+x \right )}=0} \]
✓ Solution by Maple
Time used: 0.359 (sec). Leaf size: 42
dsolve(diff(y(x),x) = (x*y(x)+y(x)+x^4*(y(x)^2+x^2)^(1/2))/x/(x+1),y(x), singsol=all)
\[ \ln \left (\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )\right )-\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (x +1\right )-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 3.021 (sec). Leaf size: 74
DSolve[y'[x] == (y[x] + x*y[x] + x^4*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x e^{\frac {1}{6} \left (-2 x^3-3 x^2-6 x-11-6 c_1\right )} \left (e^{x^2} (x+1)^2-e^{\frac {2 x^3}{3}+2 x+\frac {11}{3}+2 c_1}\right )}{2 (x+1)} \]