73.15.75 problem 22.15 (b)

Internal problem ID [15506]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.15 (b)
Date solved : Tuesday, January 28, 2025 at 08:00:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {50}{x^{3}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 23

dsolve(2*x^2*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=50/x^3,y(x), singsol=all)
 

\[ y = \frac {14 c_{2} x^{{7}/{2}}+14 c_{1} x^{4}+25}{14 x^{3}} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 25

DSolve[2*x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==50/x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {25}{14 x^3}+c_1 \sqrt {x}+c_2 x \]