81.6.2 problem 2

Internal problem ID [18685]
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 : 2
Date solved : Tuesday, January 28, 2025 at 12:10:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }-8 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

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

\[ y \left (x \right ) = c_{2} x^{2}+\frac {c_{1}}{x^{4}}-\frac {x}{5} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

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

\[ y(x)\to \frac {c_1}{x^4}+c_2 x^2-\frac {x}{5} \]