Internal problem ID [4702]
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]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+5 y^{\prime }-3 y-\theta \left (x -4\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 70
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)
\[ y \relax (x ) = \frac {\theta \left (x -4\right ) \left (5 \,{\mathrm e}^{\frac {\left (x -4\right ) \left (-5+\sqrt {37}\right )}{2}} \sqrt {37}+37 \,{\mathrm e}^{\frac {\left (x -4\right ) \left (-5+\sqrt {37}\right )}{2}}-5 \,{\mathrm e}^{-\frac {\left (x -4\right ) \left (5+\sqrt {37}\right )}{2}} \sqrt {37}+37 \,{\mathrm e}^{-\frac {\left (x -4\right ) \left (5+\sqrt {37}\right )}{2}}-74\right )}{222} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 65
DSolve[{y''[x]+5*y'[x]-3*y[x]==UnitStep[x-4],{y[0]==0,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to {cc} \{ & {cc} \frac {1}{111} e^{-\frac {5}{2} (x-4)} \left (37 \cosh \left (\frac {1}{2} \sqrt {37} (x-4)\right )+5 \sqrt {37} \sinh \left (\frac {1}{2} \sqrt {37} (x-4)\right )\right )-\frac {1}{3} & x>4 \\ 0 & \text {True} \\ \\ \\ \\ \\ \end{align*}