81.6.9 problem 9

Internal problem ID [18692]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 12:10:30 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 25

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

\[ y \left (x \right ) = \frac {x^{3}+6 c_{1} x +6 c_{2}}{6 x^{2}+6} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 28

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

\[ y(x)\to \frac {x^3+6 c_2 x+6 c_1}{6 x^2+6} \]