Internal problem ID [15336]
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: 567.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+y^{\prime }=\cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+diff(y(x),x)=cos(x)^2+exp(x)+x^2,y(x), singsol=all)
\[ y \left (x \right ) = -x^{2}+\frac {x^{3}}{3}-c_{1} {\mathrm e}^{-x}+\frac {{\mathrm e}^{x}}{2}-\frac {\cos \left (2 x \right )}{10}+\frac {\sin \left (2 x \right )}{20}+\frac {5 x}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.529 (sec). Leaf size: 55
DSolve[y''[x]+y'[x]==Cos[x]^2+Exp[x]+x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} \left (x \left (2 x^2-6 x+15\right )+3 e^x\right )+\frac {1}{20} \sin (2 x)-\frac {1}{10} \cos (2 x)-c_1 e^{-x}+c_2 \]