Internal problem ID [15345]
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: 576.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+2 y={\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+2*y(x)=exp(x)*sin(x/2)^2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (-4 c_{1} +\frac {1}{2}\right ) \cos \left (x \right )-2+\left (x -4 c_{2} \right ) \sin \left (x \right )\right ) {\mathrm e}^{x}}{4} \]
✓ Solution by Mathematica
Time used: 0.056 (sec). Leaf size: 33
DSolve[y''[x]-2*y'[x]+2*y[x]==Exp[x]*Sin[x/2]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{8} e^x ((1-8 c_2) \cos (x)+2 (x-4 c_1) \sin (x)-4) \]