78.8.21 problem 21

Internal problem ID [18219]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 11:39:59 AM
CAS classification : [_linear]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }+2 y x&=4 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y = \frac {x^{4}+c_{1}}{x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 19

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

\[ y(x)\to \frac {x^4+c_1}{x^2+1} \]