Internal problem ID [1178]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-y^{\prime } x -3 y-x^{\frac {3}{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=x^(3/2),y(x), singsol=all)
\[ y \relax (x ) = x^{3} c_{2}-\frac {4 x^{\frac {3}{2}}}{15}+\frac {c_{1}}{x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 27
DSolve[x^2*y''[x]-x*y'[x]-3*y[x]==x^(3/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {4 x^{3/2}}{15}+c_2 x^3+\frac {c_1}{x} \\ \end{align*}