Internal problem ID [11695]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number: 12.1 (ii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=0,y(0) = 0, D(y)(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = 3 \,{\mathrm e}^{2 x} x \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 13
DSolve[{y''[x]-4*y'[x]+4*y[x]==0,{y[0]==0,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 e^{2 x} x \]