Internal problem ID [11836]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y={\mathrm e}^{x} \tan \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=exp(x)*tan(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (4 c_{2} \sin \left (2 x \right )-\ln \left (\sec \left (2 x \right )+\tan \left (2 x \right )\right ) \cos \left (2 x \right )+4 \cos \left (2 x \right ) c_{1} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 42
DSolve[y''[x]-2*y'[x]+5*y[x]==Exp[x]*Tan[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{4} e^x (\cos (2 x) \text {arctanh}(\sin (2 x))-4 c_2 \cos (2 x)+(1-4 c_1) \sin (2 x)) \]