3.17 problem Example 3.46

Internal problem ID [5120]

Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page 181
Problem number: Example 3.46.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+3 y-x^{3}=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=x^3,y(x), singsol=all)
 

\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+c_{1} {\mathrm e}^{3 x}+\frac {x^{3}}{3}+\frac {4 x^{2}}{3}+\frac {26 x}{9}+\frac {80}{27} \]

Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 36

DSolve[y''[x]-4*y'[x]+3*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{9} x (3 x (x+4)+26)+c_1 e^x+c_2 e^{3 x}+\frac {80}{27} \\ \end{align*}