64.11.12 problem 12

Internal problem ID [13462]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 05:44:33 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y&=3 x^{3}-8 x \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 39

dsolve(4*diff(y(x),x$3)-4*diff(y(x),x$2)-5*diff(y(x),x)+3*y(x)=3*x^3-8*x,y(x), singsol=all)
 

\[ y = \left (c_{2} {\mathrm e}^{\frac {3 x}{2}}+c_{3} {\mathrm e}^{\frac {5 x}{2}}+\left (x^{3}+5 x^{2}+22 x +42\right ) {\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 46

DSolve[4*D[y[x],{x,3}]-4*D[y[x],{x,2}]-5*D[y[x],x]+3*y[x]==3*x^3-8*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3+5 x^2+22 x+c_1 e^{x/2}+c_2 e^{3 x/2}+c_3 e^{-x}+42 \]