73.17.36 problem 36

Internal problem ID [15570]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 36
Date solved : Tuesday, January 28, 2025 at 08:02:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-12 y^{\prime }+36 y&=3 x \,{\mathrm e}^{6 x}-2 \,{\mathrm e}^{6 x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-12*diff(y(x),x)+36*y(x)=3*x*exp(6*x)-2*exp(6*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{6 x} \left (c_{2} +c_{1} x +\frac {1}{2} x^{3}-x^{2}+\frac {4}{9} x \right ) \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 32

DSolve[D[y[x],{x,2}]-12*D[y[x],x]+36*y[x]==3*x*Exp[6*x]-2*Exp[6*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{6 x} \left (x^3-2 x^2+2 c_2 x+2 c_1\right ) \]