Internal problem ID [191]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.2, second order linear equations. Page 311
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+2 y-2 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.011 (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)
\[ y \relax (x ) = \left (3 \cos \relax (x )+4 \sin \relax (x )\right ) {\mathrm e}^{x}+x +1 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 21
DSolve[{y''[x]-2*y'[x]+2*y[x]==2*x,{y[0]==4,y'[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x+e^x (4 \sin (x)+3 \cos (x))+1 \\ \end{align*}