4.7.8 \(\left (a^2+x^2\right ) y'(x)=b+x y(x)\)

ODE
\[ \left (a^2+x^2\right ) y'(x)=b+x y(x) \] ODE Classification

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.017577 (sec), leaf count = 26

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

Maple
cpu = 0.011 (sec), leaf count = 22

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

DSolve[(a^2 + x^2)*y'[x] == b + x*y[x],y[x],x]

Mathematica raw output

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

Maple raw input

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

Maple raw output

y(x) = 1/a^2*x*b+(a^2+x^2)^(1/2)*_C1