64.12.20 problem 20

Internal problem ID [13524]
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 : 20
Date solved : Tuesday, January 28, 2025 at 05:51:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 17

dsolve((x+1)^2*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+2*y(x)=1,y(x), singsol=all)
 

\[ y = \left (x +1\right )^{2} c_{2} +\frac {1}{2}+c_{1} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 23

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

\[ y(x)\to c_2 (x+1)^2+c_1 (x+1)+\frac {1}{2} \]