Internal problem ID [7456]
Book: Second order enumerated odes
Section: section 2
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}=x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 50
dsolve(diff(y(x),x$2)-1/sqrt(x)*diff(y(x),x)+1/(4*x^2)*(x+sqrt(x)-8)*y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {560 x^{\frac {3}{2}}+28 x^{\frac {5}{2}}+\left (c_{1} x^{3}+c_{2} \right ) {\mathrm e}^{\sqrt {x}}+4 x^{3}+140 x^{2}+1680 x +3360 \sqrt {x}+3360}{x} \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 63
DSolve[y''[x]-1/Sqrt[x]*y'[x]+1/(4*x^2)*(x+Sqrt[x]-8)*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-2 x^{7/2}+x^3 \left (-2+c_2 e^{\sqrt {x}}\right )+2 e^{\sqrt {x}} \Gamma \left (8,\sqrt {x}\right )+3 c_1 e^{\sqrt {x}}}{3 x} \]