3.16 problem Problem 16

Internal problem ID [2145]

Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number: Problem 16.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

Solve \begin {gather*} \boxed {y^{\prime }+\frac {2 y}{x}-4 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 2] \end {align*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve([diff(y(x),x)+2/x*y(x)=4*x,y(1) = 2],y(x), singsol=all)
 

\[ y \relax (x ) = \frac {x^{4}+1}{x^{2}} \]

Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 12

DSolve[{y'[x]+2/x*y[x]==4*x,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^2+\frac {1}{x^2} \\ \end{align*}