Internal problem ID [4348]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page
435
Problem number: 21.
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 }+y-3 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(x^2*diff(y(x),x$2)+y(x)=3*x^2,y(x), singsol=all)
\[ y \relax (x ) = \sqrt {x}\, \sin \left (\frac {\sqrt {3}\, \ln \relax (x )}{2}\right ) c_{2}+\sqrt {x}\, \cos \left (\frac {\sqrt {3}\, \ln \relax (x )}{2}\right ) c_{1}+x^{2} \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 47
DSolve[x^2*y''[x]+y[x]==3*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {x} \left (x^{3/2}+c_1 \cos \left (\frac {1}{2} \sqrt {3} \log (x)\right )+c_2 \sin \left (\frac {1}{2} \sqrt {3} \log (x)\right )\right ) \\ \end{align*}