Internal problem ID [1174]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (-16 x^{2}+3\right ) y-8 x^{\frac {5}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 28
dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(3-16*x^2)*y(x)=8*x^(5/2),y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, \sinh \left (2 x \right ) c_{2}+\sqrt {x}\, \cosh \left (2 x \right ) c_{1}-\frac {\sqrt {x}}{2} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 39
DSolve[4*x^2*y''[x]-4*x*y'[x]+(3-16*x^2)*y[x]==8*x^(5/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-2 x} \sqrt {x} \left (-2 e^{2 x}+c_2 e^{4 x}+4 c_1\right ) \\ \end{align*}