2.192   ODE No. 192

\[ \sqrt {a^2+x^2} y'(x)-\sqrt {a^2+x^2}+y(x)+x=0 \]

✓ Mathematica : cpu = 0.138556 (sec), leaf count = 97

DSolve[x - Sqrt[a^2 + x^2] + y[x] + Sqrt[a^2 + x^2]*Derivative[1][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to a \log \left (a x^2 \sqrt {\frac {a^2}{a^2+x^2}}+a^2 x+a^3 \sqrt {\frac {a^2}{a^2+x^2}}\right ) e^{-\tanh ^{-1}\left (\frac {x}{\sqrt {a^2+x^2}}\right )}+c_1 e^{-\tanh ^{-1}\left (\frac {x}{\sqrt {a^2+x^2}}\right )}\right \}\right \}\]

✓ Maple : cpu = 0.024 (sec), leaf count = 36

dsolve((a^2+x^2)^(1/2)*diff(y(x),x)+y(x)-(a^2+x^2)^(1/2)+x = 0,y(x))
 

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