Internal problem ID [13843]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 y^{\prime \prime }-12 y^{\prime }+9 y=x \,{\mathrm e}^{\frac {3 x}{2}}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = {\mathrm e}^{\frac {3 x}{2}} \left (c_{2} +c_{1} x +\frac {1}{24} x^{3}\right ) \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 29
DSolve[4*y''[x]-12*y'[x]+9*y[x]==x*Exp[3*x/2],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{24} e^{3 x/2} \left (x^3+24 c_2 x+24 c_1\right ) \]