64.11.20 problem 20

Internal problem ID [13470]
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 : 20
Date solved : Tuesday, January 28, 2025 at 05:44:41 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 34

dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+5*diff(y(x),x)-2*y(x)=3*x^2*exp(x)-7*exp(x),y(x), singsol=all)
 

\[ y = -\frac {{\mathrm e}^{x} \left (x^{4}+4 x^{3}-4 \,{\mathrm e}^{x} c_{2} -4 c_{3} x -2 x^{2}-4 c_{1} \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 73

DSolve[D[y[x],{x,3}]-4*D[y[x],{x,2}]+5*D[y[x],x]-2*y[x]==3*x^2*Exp[x]-7*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^x \left (4 e^x \int _1^xe^{-K[1]} \left (3 K[1]^2-7\right )dK[1]-x^4-4 x^3+14 x^2+4 (7+c_2) x+4 \left (c_3 e^x+c_1\right )\right ) \]