8.8.4 problem 24

Internal problem ID [841]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.2, second order linear equations. Page 311
Problem number : 24
Date solved : Wednesday, February 05, 2025 at 04:29:56 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 19

dsolve([diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=2*x,y(0) = 4, D(y)(0) = 8],y(x), singsol=all)
 

\[ y = x +1+\left (3 \cos \left (x \right )+4 \sin \left (x \right )\right ) {\mathrm e}^{x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 22

DSolve[{D[y[x],{x,2}]-2*D[y[x],x]+2*y[x]==2*x,{y[0]==4,Derivative[1][y][0] ==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+4 e^x \sin (x)+3 e^x \cos (x)+1 \]