Internal problem ID [189]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.2, second order linear equations. Page 311
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y-12=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = 10] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(x),x$2)-4*y(x)=12,y(0) = 0, D(y)(0) = 10],y(x), singsol=all)
\[ y \relax (x ) = -{\mathrm e}^{-2 x}+4 \,{\mathrm e}^{2 x}-3 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 19
DSolve[{y''[x]-4*y[x]==12,{y[0]==0,y'[0]==10}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 5 \sinh (2 x)+3 \cosh (2 x)-3 \\ \end{align*}