4.8.45 \(\sqrt {a^2+x^2} y'(x)+y(x)+x=\sqrt {a^2+x^2}\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.025351 (sec), leaf count = 42

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

Maple
cpu = 0.015 (sec), leaf count = 36

\[ \left \{ y \relax (x ) ={1 \left ({a}^{2}\ln \left (x+\sqrt {{a}^{2}+{x}^{2}} \right ) +{\it \_C1} \right ) \left (x+\sqrt {{a}^{2}+{x}^{2}} \right ) ^{-1}} \right \} \] Mathematica raw input

DSolve[x + y[x] + Sqrt[a^2 + x^2]*y'[x] == Sqrt[a^2 + x^2],y[x],x]

Mathematica raw output

{{y[x] -> (C[1] + a^2*Log[x + Sqrt[a^2 + x^2]])/(x + Sqrt[a^2 + x^2])}}

Maple raw input

dsolve(diff(y(x),x)*(a^2+x^2)^(1/2)+x+y(x) = (a^2+x^2)^(1/2), y(x),'implicit')

Maple raw output

y(x) = (a^2*ln(x+(a^2+x^2)^(1/2))+_C1)/(x+(a^2+x^2)^(1/2))