Internal problem ID [11768]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.2. The homogeneous linear equation with constant coefficients.
Exercises page 135
Problem number: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {4 y^{\prime \prime }+4 y^{\prime }+37 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve([4*diff(y(x),x$2)+4*diff(y(x),x)+37*y(x)=0,y(0) = 2, D(y)(0) = -4],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \left (-\sin \left (3 x \right )+2 \cos \left (3 x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 26
DSolve[{4*y''[x]+4*y'[x]+37*y[x]==0,{y[0]==2,y'[0]==-4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x/2} (2 \cos (3 x)-\sin (3 x)) \]