48.3.17 problem Example 3.46

Internal problem ID [7541]
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
Date solved : Monday, January 27, 2025 at 03:04:57 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+3 y&=x^{3} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 39

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+3*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{27} \left (9 x^3+36 x^2+78 x+80\right )+c_1 e^x+c_2 e^{3 x} \]