Internal problem ID [11878]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y=-6 x^{3}+4 x^{2}} \] With initial conditions \begin {align*} [y \left (2\right ) = 4, y^{\prime }\left (2\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+4*y(x)=4*x^2-6*x^3,y(2) = 4, D(y)(2) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {23}{24} x^{4}+3 x^{3}-2 x^{2}+\frac {5}{3} x \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 28
DSolve[{x^2*y''[x]-4*x*y'[x]+4*y[x]==4*x^2-6*x^3,{y[2]==4,y'[2]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {23 x^4}{24}+3 x^3-2 x^2+\frac {5 x}{3} \]