Internal problem ID [172]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.1, second order linear equations. Page 299
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 2, y^{\prime }\left (1\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=0,y(1) = 2, D(y)(1) = 3],y(x), singsol=all)
\[ y \left (x \right ) = 3 \sin \left (\ln \left (x \right )\right )+2 \cos \left (\ln \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 16
DSolve[{x^2*y''[x]+x*y'[x]+y[x]==0,{y[1]==2,y'[1]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 \sin (\log (x))+2 \cos (\log (x)) \]