ODE
\[ \left (a^2+x^2\right ) y'(x)=b+x y(x) \] ODE Classification
[_linear]
Book solution method
Linear ODE
Mathematica ✓
cpu = 0.181525 (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
\[\left [y \left (x \right ) = \frac {x b}{a^{2}}+\sqrt {a^{2}+x^{2}}\, \textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = 1/a^2*x*b+(a^2+x^2)^(1/2)*_C1]