ODE
\[ x^2 y''(x)=a+b x \] ODE Classification
[[_2nd_order, _quadrature]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.00876634 (sec), leaf count = 26
\[\left \{\left \{y(x)\to \log (x) (b x-a)-b x+c_2 x+c_1\right \}\right \}\]
Maple ✓
cpu = 0.013 (sec), leaf count = 23
\[ \left \{ y \left ( x \right ) = \left ( bx-a \right ) \ln \left ( x \right ) + \left ( -b+{\it \_C1} \right ) x+{\it \_C2} \right \} \] Mathematica raw input
DSolve[x^2*y''[x] == a + b*x,y[x],x]
Mathematica raw output
{{y[x] -> -(b*x) + C[1] + x*C[2] + (-a + b*x)*Log[x]}}
Maple raw input
dsolve(x^2*diff(diff(y(x),x),x) = b*x+a, y(x),'implicit')
Maple raw output
y(x) = (b*x-a)*ln(x)+(-b+_C1)*x+_C2