Internal problem ID [11717]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page
113
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(0) = 1, D(y)(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (3 x +1\right ) \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 14
DSolve[{y''[x]-2*y'[x]+y[x]==0,{y[0]==1,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (3 x+1) \]