82.10.5 problem Ex. 5

Internal problem ID [18760]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter II. Equations of the first order and of the first degree. Exercises at page 27
Problem number : Ex. 5
Date solved : Tuesday, January 28, 2025 at 12:15:21 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 25

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

\[ y(x)\to \frac {4 x^3+3 c_1}{3 x^2+3} \]