7.4.24 problem 24

Internal problem ID [96]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.5 (linear equations). Problems at page 54
Problem number : 24
Date solved : Friday, February 07, 2025 at 07:49:16 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+4\right ) y^{\prime }+3 x y&=x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 15

dsolve([(x^2+4)*diff(y(x),x)+3*x*y(x)=x,y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {1}{3}+\frac {16}{3 \left (x^{2}+4\right )^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 22

DSolve[{(x^2+4)*D[y[x],x]+3*x*y[x]==x,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {16}{3 \left (x^2+4\right )^{3/2}}+\frac {1}{3} \]