ODE
\[ 4 x^2 y''(x)-\left (4 x^2+1\right ) y(x)+4 x y'(x)=4 e^x x^{3/2} \] ODE Classification
[[_2nd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.0538405 (sec), leaf count = 39
\[\left \{\left \{y(x)\to \frac {e^{-x} \left (e^{2 x} \left (2 c_2+2 x-1\right )+4 c_1\right )}{4 \sqrt {x}}\right \}\right \}\]
Maple ✓
cpu = 0.068 (sec), leaf count = 24
\[ \left \{ y \left ( x \right ) ={\frac {x{{\rm e}^{x}}+2\,\cosh \left ( x \right ) {\it \_C1}+2\,\sinh \left ( x \right ) {\it \_C2}}{2}{\frac {1}{\sqrt {x}}}} \right \} \] Mathematica raw input
DSolve[-((1 + 4*x^2)*y[x]) + 4*x*y'[x] + 4*x^2*y''[x] == 4*E^x*x^(3/2),y[x],x]
Mathematica raw output
{{y[x] -> (4*C[1] + E^(2*x)*(-1 + 2*x + 2*C[2]))/(4*E^x*Sqrt[x])}}
Maple raw input
dsolve(4*x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-(4*x^2+1)*y(x) = 4*exp(x)*x^(3/2), y(x),'implicit')
Maple raw output
y(x) = 1/2*(x*exp(x)+2*cosh(x)*_C1+2*sinh(x)*_C2)/x^(1/2)