Internal problem ID [14880]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 59.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+y(x)=0,y(1) = 1, D(y)(1) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {2}{\sqrt {x}}-\frac {1}{x} \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 18
DSolve[{2*x^2*y''[x]+5*x*y'[x]+y[x]==0,{y[1]==1,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 \sqrt {x}-1}{x} \]