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]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y=2 x} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 8] \end {align*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \left (3 \cos \left (x \right )+4 \sin \left (x \right )\right ) {\mathrm e}^{x}+x +1 \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 22
DSolve[{y''[x]-2*y'[x]+2*y[x]==2*x,{y[0]==4,y'[0]==8}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+4 e^x \sin (x)+3 e^x \cos (x)+1 \]