74.18.53 problem 59

Internal problem ID [16610]
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
Date solved : Tuesday, January 28, 2025 at 09:12:42 AM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (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)
 

\[ y = -\frac {1}{x}+\frac {2}{\sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 18

DSolve[{2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+y[x]==0,{y[1]==1,Derivative[1][y][1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 \sqrt {x}-1}{x} \]