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 = 0.177353 (sec), leaf count = 22

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

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

\[\left [y \left (x \right ) = -\frac {a}{\left (b +1\right ) x}+x^{b} \textit {\_C1}\right ]\] 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))

Maple raw output

[y(x) = -1/(b+1)/x*a+x^b*_C1]