74.5.16 problem 16

Internal problem ID [15980]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 08:25:30 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(y(x),x)-9*x/(9*x^2+49)*y(x)=x,y(x), singsol=all)
 

\[ y = x^{2}+\frac {49}{9}+\sqrt {9 x^{2}+49}\, c_{1} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 26

DSolve[D[y[x],x]-9*x/(9*x^2+49)*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+c_1 \sqrt {9 x^2+49}+\frac {49}{9} \]