82.39.9 problem Ex. 9

Internal problem ID [18941]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 9
Date solved : Tuesday, January 28, 2025 at 12:37:33 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=x^{m} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 26

dsolve(x^2*diff(y(x),x$2)-3*x*diff(y(x),x)+4*y(x)=x^m,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 30

DSolve[x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x]==x^m,y[x],x,IncludeSingularSolutions -> True]
 

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