Internal problem ID [8441]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, Additional non-linear first order
Problem number: 863.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
\[ \boxed {y^{\prime }-\frac {y+x \sqrt {y^{2}+x^{2}}+x^{3} \sqrt {y^{2}+x^{2}}+x^{4} \sqrt {y^{2}+x^{2}}}{x}=0} \]
✓ Solution by Maple
Time used: 1.125 (sec). Leaf size: 38
dsolve(diff(y(x),x) = (y(x)+x*(y(x)^2+x^2)^(1/2)+x^3*(y(x)^2+x^2)^(1/2)+x^4*(y(x)^2+x^2)^(1/2))/x,y(x), singsol=all)
\[ \ln \left (\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )\right )-\frac {x^{4}}{4}-\frac {x^{3}}{3}-x -\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.483 (sec). Leaf size: 26
DSolve[y'[x] == (y[x] + x*Sqrt[x^2 + y[x]^2] + x^3*Sqrt[x^2 + y[x]^2] + x^4*Sqrt[x^2 + y[x]^2])/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x \sinh \left (\frac {x^4}{4}+\frac {x^3}{3}+x+c_1\right ) \\ \end{align*}