29.26.2 problem 734

Internal problem ID [5323]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 734
Date solved : Monday, January 27, 2025 at 11:12:37 AM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.126 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.292 (sec). Leaf size: 27

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

\[ \text {Solve}\left [\arctan \left (\frac {x}{y(x)}\right )+\sqrt {x^2+y(x)^2+1}=c_1,y(x)\right ] \]