73.4.26 problem 5.3 (f)

Internal problem ID [15108]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 5. LINEAR FIRST ORDER EQUATIONS. Additional exercises. page 103
Problem number : 5.3 (f)
Date solved : Tuesday, January 28, 2025 at 07:31:01 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (2\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 21

dsolve([(1+x^2)*diff(y(x),x)=x*(3+3*x^2-y(x)),y(2) = 8],y(x), singsol=all)
 

\[ y = x^{2}+1+\frac {3 \sqrt {5}}{\sqrt {x^{2}+1}} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 26

DSolve[{(1+x^2)*D[y[x],x]==x*(3+3*x^2-y[x]),{y[2]==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+\frac {3 \sqrt {5}}{\sqrt {x^2+1}}+1 \]