2.1061   ODE No. 1061

\[ -e^{-\frac {x^{3/2}}{3}} x+y''(x)+\sqrt {x} y'(x)+\left (\frac {x}{4}+\frac {1}{4 \sqrt {x}}-9\right ) y(x)=0 \]

✓ Mathematica : cpu = 0.0641201 (sec), leaf count = 70

DSolve[-(x/E^(x^(3/2)/3)) + (-9 + 1/(4*Sqrt[x]) + x/4)*y[x] + Sqrt[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to -\frac {1}{9} e^{3 x-\frac {1}{3} \left (\sqrt {x}+9\right ) x} x+c_1 e^{-\frac {1}{3} \left (\sqrt {x}+9\right ) x}+\frac {1}{6} c_2 e^{6 x-\frac {1}{3} \left (\sqrt {x}+9\right ) x}\right \}\right \}\]

✓ Maple : cpu = 0.168 (sec), leaf count = 28

dsolve(diff(diff(y(x),x),x)+diff(y(x),x)*x^(1/2)+(1/4/x^(1/2)+1/4*x-9)*y(x)-x*exp(-1/3*x^(3/2))=0,y(x))
 

\[y \left (x \right ) = -\frac {{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}} \left (-9 \cosh \left (3 x \right ) c_{1} -9 \sinh \left (3 x \right ) c_{2} +x \right )}{9}\]