60.2.229 problem 805

Internal problem ID [10816]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 805
Date solved : Tuesday, January 28, 2025 at 05:17:05 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} y^{\prime }&=\frac {y x +y+x^{4} \sqrt {x^{2}+y^{2}}}{x \left (1+x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.336 (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)
 

\[ \ln \left (\sqrt {x^{2}+y^{2}}+y\right )-\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (x +1\right )-\ln \left (x \right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.355 (sec). Leaf size: 29

DSolve[D[y[x],x] == (y[x] + x*y[x] + x^4*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \sinh \left (\int _1^x\frac {K[1]^3}{K[1]+1}dK[1]+c_1\right ) \]