73.9.27 problem 14.3 (c)

Internal problem ID [15288]
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 : 14.3 (c)
Date solved : Tuesday, January 28, 2025 at 07:51:36 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=\sqrt {x} \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=sqrt(x),x],singsol=all)
 

\[ y = \frac {3 c_{2} x^{2}-4 x^{{3}/{2}}+3 c_{1}}{3 x} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==Sqrt[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {4 \sqrt {x}}{3}+\frac {c_1}{x}+c_2 x \]