73.17.45 problem 45

Internal problem ID [15579]
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 : 45
Date solved : Tuesday, January 28, 2025 at 08:02:41 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime }-12 y^{\prime }+9 y&=x \,{\mathrm e}^{\frac {3 x}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

dsolve(4*diff(y(x),x$2)-12*diff(y(x),x)+9*y(x)=x*exp(3*x/2),y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {3 x}{2}} \left (c_{2} +c_{1} x +\frac {1}{24} x^{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 29

DSolve[4*D[y[x],{x,2}]-12*D[y[x],x]+9*y[x]==x*Exp[3*x/2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{24} e^{3 x/2} \left (x^3+24 c_2 x+24 c_1\right ) \]