Internal problem ID [15347]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Superposition principle. Exercises page 137
Problem number: 578.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y={\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+5*y(x)=exp(x)*(1-2*sin(x)^2)+10*x+1,y(x), singsol=all)
\[ y \left (x \right ) = \frac {{\mathrm e}^{x} \left (x +4 c_{2} \right ) \sin \left (2 x \right )}{4}+{\mathrm e}^{x} \cos \left (2 x \right ) c_{1} +2 x +1 \]
✓ Solution by Mathematica
Time used: 1.163 (sec). Leaf size: 44
DSolve[y''[x]-2*y'[x]+5*y[x]==Exp[x]*(1-2*Sin[x]^2)+10*x+1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x+\frac {1}{16} (1+16 c_2) e^x \cos (2 x)+\frac {1}{4} e^x (x+4 c_1) \sin (2 x)+1 \]