Internal problem ID [5210]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 24. Solutions of linear DE by Laplace transforms. Supplementary Problems.
page 248
Problem number: Problem 24.33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }-3 y=\operatorname {Heaviside}\left (-4+x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.531 (sec). Leaf size: 45
dsolve([diff(y(x),x$2)+5*diff(y(x),x)-3*y(x)=Heaviside(x-4),y(0) = 0, D(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\operatorname {Heaviside}\left (x -4\right ) \left (-1+\frac {5 \sqrt {37}\, \sinh \left (\frac {\left (x -4\right ) \sqrt {37}}{2}\right ) {\mathrm e}^{-\frac {5 x}{2}+10}}{37}+\cosh \left (\frac {\left (x -4\right ) \sqrt {37}}{2}\right ) {\mathrm e}^{-\frac {5 x}{2}+10}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 70
DSolve[{y''[x]+5*y'[x]-3*y[x]==UnitStep[x-4],{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{222} \left (-74+\left (37+5 \sqrt {37}\right ) e^{\frac {1}{2} \left (-5+\sqrt {37}\right ) (x-4)}+\left (37-5 \sqrt {37}\right ) e^{-\frac {1}{2} \left (5+\sqrt {37}\right ) (x-4)}\right ) & x>4 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]