75.18.2 problem 591

Internal problem ID [17090]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Initial value problem. Exercises page 140
Problem number : 591
Date solved : Tuesday, January 28, 2025 at 09:52:01 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+9 y&=9 x^{2}-12 x +2 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.016 (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)
 

\[ y = {\mathrm e}^{3 x}+x^{2} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 14

DSolve[{D[y[x],{x,2}]-6*D[y[x],x]+9*y[x]==9*x^2-12*x+2,{y[0]==1,Derivative[1][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2+e^{3 x} \]