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

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

[[_homogeneous, `class A`], _rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0163454 (sec), leaf count = 31

\[\left \{\left \{y(x)\to -\frac {(a-1) x^{a+1}}{b x^a-(a-1) c_1 x}\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 26

\[ \left \{ {\frac {b}{x \left (a-1 \right ) }}-{x}^{-a}{\it \_C1}+ \left (y \relax (x ) \right ) ^{-1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

1/x/(a-1)*b-x^(-a)*_C1+1/y(x) = 0