75.16.66 problem 539

Internal problem ID [17039]
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. Trial and error method. Exercises page 132
Problem number : 539
Date solved : Tuesday, January 28, 2025 at 09:47:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=\left (x^{2}+x \right ) {\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(diff(y(x),x$2)-3*diff(y(x),x)+2*y(x)=(x+x^2)*exp(3*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{x} \left (\left (x^{2}-2 x +2\right ) {\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} c_{1} +2 c_{2} \right )}{2} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-3*D[y[x],x]+2*y[x]==(x+x^2)*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{3 x} \left (x^2-2 x+2\right )+c_1 e^x+c_2 e^{2 x} \]