Internal problem ID [1165]
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: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{\frac {5}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=x^(5/2),y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+x^{3} c_{1}-4 x^{\frac {5}{2}} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 23
DSolve[x^2*y''[x]-4*x*y'[x]+6*y[x]==x^(5/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 \left (-4 \sqrt {x}+c_2 x+c_1\right ) \\ \end{align*}