Internal problem ID [11724]
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: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1+x \right )^{2} y^{\prime \prime }-3 \left (1+x \right ) y^{\prime }+3 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= 1+x \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([(x+1)^2*diff(y(x),x$2)-3*(x+1)*diff(y(x),x)+3*y(x)=0,x+1],singsol=all)
\[ y \left (x \right ) = \left (1+x \right ) \left (c_{1} +c_{2} \left (1+x \right )^{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 20
DSolve[(x+1)^2*y''[x]-3*(x+1)*y'[x]+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 (x+1)^3+c_1 (x+1) \]