Internal problem ID [8641]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1061.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime } \sqrt {x}+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{\frac {3}{2}}}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 38
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), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x^{\frac {3}{2}}}{3}} \sinh \left (3 x \right ) c_{2}+{\mathrm e}^{-\frac {x^{\frac {3}{2}}}{3}} \cosh \left (3 x \right ) c_{1}-\frac {x \,{\mathrm e}^{-\frac {x^{\frac {3}{2}}}{3}}}{9} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 45
DSolve[-(x/E^(x^(3/2)/3)) + (-9 + 1/(4*Sqrt[x]) + x/4)*y[x] + Sqrt[x]*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{18} e^{-\frac {1}{3} \left (\sqrt {x}+9\right ) x} \left (-2 e^{3 x} x+3 c_2 e^{6 x}+18 c_1\right ) \\ \end{align*}