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]]
\[ \boxed {x^{2} y^{\prime \prime }-y^{\prime } x -3 y=x^{\frac {3}{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=x^(3/2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {15 c_{2} x^{4}-4 x^{\frac {5}{2}}+15 c_{1}}{15 x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 27
DSolve[x^2*y''[x]-x*y'[x]-3*y[x]==x^(3/2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {4 x^{3/2}}{15}+c_2 x^3+\frac {c_1}{x} \]