29.7.18 problem 193

Internal problem ID [4793]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 193
Date solved : Monday, January 27, 2025 at 09:38:14 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+2 y&=\sqrt {1+y^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (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: 60.245 (sec). Leaf size: 2509

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

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