20.3.16 problem Problem 16

Internal problem ID [3625]
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
Date solved : Monday, January 27, 2025 at 07:47:46 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=4 x \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

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

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

\[ y(x)\to x^2+\frac {1}{x^2} \]