Internal problem ID [1175]
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: 21.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 x^{2} y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}+3\right ) y-x^{\frac {7}{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(4*x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+(4*x^2+3)*y(x)=x^(7/2),y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {x}\, \sin \left (x \right ) c_{2} +\sqrt {x}\, \cos \left (x \right ) c_{1} +\frac {x^{\frac {3}{2}}}{4} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 40
DSolve[4*x^2*y''[x]-4*x*y'[x]+(4*x^2+3)*y[x]==x^(7/2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \sqrt {x} \left (x+4 c_1 e^{-i x}-2 i c_2 e^{i x}\right ) \\ \end{align*}