Internal problem ID [13540]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.2 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_Emden, _Fowler]]
\[ \boxed {4 x^{2} y^{\prime \prime }+y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \sqrt {x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([4*x^2*diff(y(x),x$2)+y(x)=0,sqrt(x)],singsol=all)
\[ y \left (x \right ) = \left (c_{1} +c_{2} \ln \left (x \right )\right ) \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 24
DSolve[4*x^2*y''[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} \sqrt {x} (c_2 \log (x)+2 c_1) \]