Internal problem ID [14588]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 13.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+34 y={\mathrm e}^{3 t} \tan \left (5 t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 40
dsolve(diff(y(t),t$2)-6*diff(y(t),t)+34*y(t)=exp(3*t)*tan(5*t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {{\mathrm e}^{3 t} \left (\ln \left (\sec \left (5 t \right )+\tan \left (5 t \right )\right ) \cos \left (5 t \right )-25 \cos \left (5 t \right ) c_{1} -25 \sin \left (5 t \right ) c_{2} \right )}{25} \]
✓ Solution by Mathematica
Time used: 0.434 (sec). Leaf size: 318
DSolve[y''[t]-6*y'[t]+4*y[t]==Exp[3*t]*Tan[5*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{210} e^{3 t} \left (-21 i \operatorname {Hypergeometric2F1}\left (1,-\frac {i}{2 \sqrt {5}},1-\frac {i}{2 \sqrt {5}},-e^{10 i t}\right )-21 i \operatorname {Hypergeometric2F1}\left (1,\frac {i}{2 \sqrt {5}},1+\frac {i}{2 \sqrt {5}},-e^{10 i t}\right )+2 \sqrt {5} e^{10 i t} \operatorname {Hypergeometric2F1}\left (1,1-\frac {i}{2 \sqrt {5}},2-\frac {i}{2 \sqrt {5}},-e^{10 i t}\right )+i e^{10 i t} \operatorname {Hypergeometric2F1}\left (1,1-\frac {i}{2 \sqrt {5}},2-\frac {i}{2 \sqrt {5}},-e^{10 i t}\right )-2 \sqrt {5} e^{10 i t} \operatorname {Hypergeometric2F1}\left (1,1+\frac {i}{2 \sqrt {5}},2+\frac {i}{2 \sqrt {5}},-e^{10 i t}\right )+i e^{10 i t} \operatorname {Hypergeometric2F1}\left (1,1+\frac {i}{2 \sqrt {5}},2+\frac {i}{2 \sqrt {5}},-e^{10 i t}\right )+210 c_1 e^{-\sqrt {5} t}+210 c_2 e^{\sqrt {5} t}\right ) \]