78.14.1 problem 1

Internal problem ID [18337]
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 : 1
Date solved : Tuesday, January 28, 2025 at 11:47:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=2 x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 17

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

\[ y = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{x}+2 x +4 \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 23

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

\[ y(x)\to c_1 e^x+x \left (2+c_2 e^x\right )+4 \]