64.12.8 problem 8

Internal problem ID [13512]
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
Date solved : Tuesday, January 28, 2025 at 05:50:33 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&={\mathrm e}^{x} \tan \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 38

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=exp(x)*tan(2*x),y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{x} \left (\ln \left (\sec \left (2 x \right )+\tan \left (2 x \right )\right ) \cos \left (2 x \right )-4 \cos \left (2 x \right ) c_{1} -4 \sin \left (2 x \right ) c_{2} \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 42

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+5*y[x]==Exp[x]*Tan[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{4} e^x (\cos (2 x) \text {arctanh}(\sin (2 x))-4 c_2 \cos (2 x)+(1-4 c_1) \sin (2 x)) \]