Internal problem ID [225]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y=\sinh \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 64
dsolve(diff(y(x),x$2)-4*y(x)=sinh(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-2 x} c_{1} +\frac {\left (-2 \sinh \left (x \right )^{2} \cosh \left (x \right )-2 \sinh \left (x \right )^{3}+\cosh \left (x \right )\right ) {\mathrm e}^{-2 x}}{12}+\frac {{\mathrm e}^{2 x} \left (\sinh \left (x \right )^{2} \cosh \left (x \right )-\sinh \left (x \right )^{3}-\frac {\cosh \left (x \right )}{2}\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 38
DSolve[y''[x]-4*y[x]==Sinh[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{-2 x} \left (e^x-e^{3 x}+6 c_1 e^{4 x}+6 c_2\right ) \]