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

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

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

Book solution method
Homogeneous equation

Mathematica ✓
cpu = 0.278299 (sec), leaf count = 23

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

Maple ✓
cpu = 0.033 (sec), leaf count = 19

\[\left [y \left (x \right ) = \frac {\tan \left (\frac {b \left (\ln \left (x \right )+\textit {\_C1} \right )}{a}\right ) x}{b}\right ]\] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

[y(x) = tan(b*(ln(x)+_C1)/a)*x/b]