Internal problem ID [12526]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 156.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+3 y={\mathrm e}^{-x} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+3*y(x)=exp(-x)*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \cos \left (x \sqrt {2}\right ) c_{1} +{\mathrm e}^{x} \sin \left (x \sqrt {2}\right ) c_{2} +\frac {5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )-\frac {4 \sin \left (x \right )}{5}\right )}{41} \]
✓ Solution by Mathematica
Time used: 1.089 (sec). Leaf size: 56
DSolve[y''[x]-2*y'[x]+3*y[x]==Exp[-x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {4}{41} e^{-x} \sin (x)+\frac {5}{41} e^{-x} \cos (x)+c_2 e^x \cos \left (\sqrt {2} x\right )+c_1 e^x \sin \left (\sqrt {2} x\right ) \]