78.14.18 problem 6 (c)

Internal problem ID [18354]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 19. The Method of Variation of Parameters. Problems at page 135
Problem number : 6 (c)
Date solved : Tuesday, January 28, 2025 at 11:48:16 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 16

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

\[ y = c_{2} x +{\mathrm e}^{x} c_{1} +x^{2}+1 \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 22

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

\[ y(x)\to x^2+x-c_2 x+c_1 e^x+1 \]