4.6.6 \(x^2 y'(x)=a+b x y(x)\)

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

[_linear]

Book solution method
Linear ODE

Mathematica
cpu = 0.00891025 (sec), leaf count = 22

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

Maple
cpu = 0.01 (sec), leaf count = 21

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

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

Mathematica raw output

{{y[x] -> -(a/(x + b*x)) + x^b*C[1]}}

Maple raw input

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

Maple raw output

y(x) = -1/(b+1)*a/x+x^b*_C1