29.7.21 problem 196

Internal problem ID [4796]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 196
Date solved : Tuesday, January 28, 2025 at 02:39:43 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 1.053 (sec). Leaf size: 28

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

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

✓ Solution by Mathematica

Time used: 0.237 (sec). Leaf size: 12

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

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