74.15.25 problem 25

Internal problem ID [16464]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 25
Date solved : Tuesday, January 28, 2025 at 09:08:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=2 x \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-6*y(x)=2*x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 23

DSolve[x^2*D[y[x],{x,2}]+2*x*D[y[x],x]-6*y[x]==2*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1}{x^3}+c_2 x^2-\frac {x}{2} \]