Internal problem ID [9792]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1465.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-a^{2} y^{\prime }+2 a^{2} y=\sinh \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 101
dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-a^2*diff(y(x),x)+2*a^2*y(x)-sinh(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 c_{3} \left (a^{4}-5 a^{2}+4\right ) {\mathrm e}^{-a x}+2 \left (a +1\right ) \left (a^{2} c_{1} +\frac {\sinh \left (3 x \right )}{6}-4 c_{1} -\frac {\cosh \left (3 x \right )}{6}\right ) \left (a -1\right ) {\mathrm e}^{2 x}+2 c_{2} \left (a^{4}-5 a^{2}+4\right ) {\mathrm e}^{a x}+a^{2} {\mathrm e}^{x}-4 \,{\mathrm e}^{x}+{\mathrm e}^{-x}}{2 a^{4}-10 a^{2}+8} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 52
DSolve[-Sinh[x] + 2*a^2*y[x] - a^2*y'[x] - 2*y''[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-x}-3 e^x}{6-6 a^2}+c_1 e^{-a x}+c_3 e^{a x}+c_2 e^{2 x} \]