Internal problem ID [11847]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-6 y^{\prime } x +10 y=3 x^{4}+6 x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\frac {3}{2} x^{4}-3 x^{3}+\frac {1}{3} c_{1} x^{5}+c_{2} x^{2} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 28
DSolve[x^2*y''[x]-6*x*y'[x]+10*y[x]==3*x^4+6*x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^5-\frac {3}{2} (x+2) x^3+c_1 x^2 \]