Internal problem ID [5405]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 40.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+5 y^{\prime }+6 y={\mathrm e}^{-2 x} \sec \left (x \right )^{2} \left (1+2 \tan \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 95
dsolve(diff(y(x),x$2)+5*diff(y(x),x)+6*y(x)=exp(-2*x)*sec(x)^2*(1+2*tan(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 \sec \left (x \right )^{2}+2 c_{2} +2 \tan \left (x \right )-6\right ) {\mathrm e}^{\left (-2+2 i\right ) x}+\left (\tan \left (x \right )^{2}+c_{2} +\tan \left (x \right )\right ) {\mathrm e}^{\left (-2+4 i\right ) x}+2 c_{1} {\mathrm e}^{\left (-3+2 i\right ) x}+c_{1} {\mathrm e}^{\left (-3+4 i\right ) x}+\left (\tan \left (x \right )^{2}+c_{2} +\tan \left (x \right )\right ) {\mathrm e}^{-2 x}+{\mathrm e}^{-3 x} c_{1}}{{\mathrm e}^{4 i x}+2 \,{\mathrm e}^{2 i x}+1} \]
✓ Solution by Mathematica
Time used: 0.147 (sec). Leaf size: 26
DSolve[y''[x]+5*y'[x]+6*y[x]==Exp[-2*x]*Sec[x]^2*(1+2*Tan[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-3 x} \left (e^x \tan (x)+c_2 e^x+c_1\right ) \]