Internal problem ID [12211]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 162.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 h y^{\prime }+y n^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = a, y^{\prime }\left (0\right ) = c] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 93
dsolve([diff(y(x),x$2)+2*h*diff(y(x),x)+n^2*y(x)=0,y(0) = a, D(y)(0) = c],y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\sqrt {h^{2}-n^{2}}\, a +h a +c \right ) {\mathrm e}^{\left (-h +\sqrt {h^{2}-n^{2}}\right ) x}-{\mathrm e}^{-\left (h +\sqrt {h^{2}-n^{2}}\right ) x} \left (-\sqrt {h^{2}-n^{2}}\, a +h a +c \right )}{2 \sqrt {h^{2}-n^{2}}} \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 123
DSolve[{y''[x]+2*h*y'[x]+n^2*y[x]==0,{y[0]==a,y'[0]==c}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-\left (x \left (\sqrt {h^2-n^2}+h\right )\right )} \left (a h \left (e^{2 x \sqrt {h^2-n^2}}-1\right )+a \sqrt {h^2-n^2} \left (e^{2 x \sqrt {h^2-n^2}}+1\right )+c \left (e^{2 x \sqrt {h^2-n^2}}-1\right )\right )}{2 \sqrt {h^2-n^2}} \]