73.10.9 problem 15.2 (i)

Internal problem ID [15304]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.2 (i)
Date solved : Tuesday, January 28, 2025 at 07:52:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 13

dsolve([(x+1)^2*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+2*y(x)=0,y(0) = 0, D(y)(0) = 4],y(x), singsol=all)
 

\[ y = 4 x^{2}+4 x \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 11

DSolve[{(x+1)^2*D[y[x],{x,2}]-2*(x+1)*D[y[x],x]+2*y[x]==0,{y[0]==0,Derivative[1][y][0] ==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 4 x (x+1) \]