78.8.37 problem 37

Internal problem ID [18235]
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 : 37
Date solved : Tuesday, January 28, 2025 at 11:43:11 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 30

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

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