64.12.19 problem 19

Internal problem ID [13523]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number : 19
Date solved : Tuesday, January 28, 2025 at 05:51:48 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-6 x y^{\prime }+10 y&=3 x^{4}+6 x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve(x^2*diff(y(x),x$2)-6*x*diff(y(x),x)+10*y(x)=3*x^4+6*x^3,y(x), singsol=all)
 

\[ y = -\frac {3}{2} x^{4}-3 x^{3}+\frac {1}{3} c_{1} x^{5}+c_{2} x^{2} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 28

DSolve[x^2*D[y[x],{x,2}]-6*x*D[y[x],x]+10*y[x]==3*x^4+6*x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^5-\frac {3}{2} (x+2) x^3+c_1 x^2 \]