Internal problem ID [11728]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page
124
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([(x^3-x^2)*diff(y(x),x$2)-(x^3+2*x^2-2*x)*diff(y(x),x)+(2*x^2+2*x-2)*y(x)=0,x^2],singsol=all)
\[ y \left (x \right ) = x \left (c_{2} {\mathrm e}^{x}+c_{1} x \right ) \]
✓ Solution by Mathematica
Time used: 0.101 (sec). Leaf size: 36
DSolve[(x^3-x^2)*y''[x]-(x^3+2*x^2-2*x)*y'[x]+(2*x^2+2*x-2)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sqrt {1-x} x \left (c_2 x-c_1 e^x\right )}{\sqrt {x-1}} \]