Internal problem ID [3449]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 193.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{\prime }+2 y-\sqrt {y^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x*diff(y(x),x)+2*y(x) = sqrt(1+y(x)^2),y(x), singsol=all)
\[ \ln \left (x \right )+\int _{}^{y \left (x \right )}-\frac {1}{-2 \textit {\_a} +\sqrt {\textit {\_a}^{2}+1}}d \textit {\_a} +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 60.221 (sec). Leaf size: 2509
DSolve[x y'[x]+2 y[x]==Sqrt[1+y[x]^2],y[x],x,IncludeSingularSolutions -> True]
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