Internal problem ID [15303]
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: 533.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-y^{\prime }={\mathrm e}^{x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)-diff(y(x),x)=exp(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 c_{1} -\cos \left (x \right )-\sin \left (x \right )\right ) {\mathrm e}^{x}}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.106 (sec). Leaf size: 24
DSolve[y''[x]-y'[x]==Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\frac {1}{2} e^x (\sin (x)+\cos (x)-2 c_1) \]