60.2.204 problem 780

Internal problem ID [10791]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 780
Date solved : Tuesday, January 28, 2025 at 05:13:42 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {y x +y+x \sqrt {x^{2}+y^{2}}}{x \left (1+x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.548 (sec). Leaf size: 32

dsolve(diff(y(x),x) = (x*y(x)+y(x)+x*(y(x)^2+x^2)^(1/2))/x/(x+1),y(x), singsol=all)
 

\[ \frac {\sqrt {x^{2}+y^{2}}+y+\left (x^{2}+x \right ) c_{1}}{x \left (x +1\right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.297 (sec). Leaf size: 15

DSolve[D[y[x],x] == (y[x] + x*y[x] + x*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \sinh (\log (x+1)+c_1) \]