Internal problem ID [12520]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 150.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=8 \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$2)+diff(y(x),x)-2*y(x)=8*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {2 \left (-\cos \left (2 x \right )-3 \sin \left (2 x \right )\right ) {\mathrm e}^{2 x}}{5}+c_{2} {\mathrm e}^{3 x}+c_{1} \right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 35
DSolve[y''[x]+y'[x]-2*y[x]==8*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-2 x}+c_2 e^x-\frac {2}{5} (3 \sin (2 x)+\cos (2 x)) \]