Internal problem ID [15360]
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. Initial value problem. Exercises page 140
Problem number: 591.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=9 x^{2}-12 x +2} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)-6*diff(y(x),x)+9*y(x)=9*x^2-12*x+2,y(0) = 1, D(y)(0) = 3],y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x}+x^{2} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 14
DSolve[{y''[x]-6*y'[x]+9*y[x]==9*x^2-12*x+2,{y[0]==1,y'[0]==3}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+e^{3 x} \]