60.2.108 problem 684

Internal problem ID [10695]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 684
Date solved : Tuesday, January 28, 2025 at 05:05:56 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {y+\sqrt {x^{2}+y^{2}}\, x^{2}}{x} \end{align*}

✓ Solution by Maple

Time used: 1.173 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.246 (sec). Leaf size: 18

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

\[ y(x)\to x \sinh \left (\frac {x^2}{2}+c_1\right ) \]