Internal problem ID [15306]
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. Trial and error method. Exercises page 132
Problem number: 536.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {4 y^{\prime \prime }+8 y^{\prime }=\sin \left (x \right ) x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(4*diff(y(x),x$2)+8*diff(y(x),x)=x*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} c_{1}}{2}+\frac {\left (-1-5 x \right ) \cos \left (x \right )}{50}+\frac {\left (-5 x +14\right ) \sin \left (x \right )}{100}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.266 (sec). Leaf size: 42
DSolve[4*y''[x]+8*y'[x]==x*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (\frac {7}{50}-\frac {x}{20}\right ) \sin (x)-\frac {1}{50} (5 x+1) \cos (x)-\frac {1}{2} c_1 e^{-2 x}+c_2 \]