64.13.15 problem 15

Internal problem ID [13545]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 05:52:24 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+8 y&=2 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)-5*x*diff(y(x),x)+8*y(x)=2*x^3,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

DSolve[x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+8*y[x]==2*x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \left (c_2 x^2-2 x+c_1\right ) \]