Internal problem ID [12489]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.4, page 265
Problem number: 4 (c).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }=\left \{\begin {array}{cc} 0 & 0\le x <1 \\ \left (x -1\right )^{2} & 1\le x \end {array}\right .} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 39
dsolve([diff(y(x),x$2)-2*diff(y(x),x)=piecewise(0<=x and x<1,0,1<=x,(x-1)^2),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \left \{\begin {array}{cc} 1 & x <1 \\ \frac {7}{8} & x =1 \\ \frac {25}{24}+\frac {{\mathrm e}^{2 x -2}}{8}+\frac {x^{2}}{4}-\frac {x^{3}}{6}-\frac {x}{4} & 1<x \end {array}\right . \]
✓ Solution by Mathematica
Time used: 0.269 (sec). Leaf size: 40
DSolve[{y''[x]-2*y'[x]==Piecewise[{ {0,0<=x<1},{(x-1)^2,x>=1}}],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 1 & x\leq 1 \\ \frac {1}{24} \left (-4 x^3+6 x^2-6 x+3 e^{2 x-2}+25\right ) & \text {True} \\ \end {array} \\ \end {array} \]