Internal problem ID [5873]
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]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+3 y=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+3*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{x} c_{1} +\frac {x^{3}}{3}+\frac {4 x^{2}}{3}+\frac {26 x}{9}+\frac {80}{27} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 39
DSolve[y''[x]-4*y'[x]+3*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{27} \left (9 x^3+36 x^2+78 x+80\right )+c_1 e^x+c_2 e^{3 x} \]