Internal problem ID [11794]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y=3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \left (x^{4}+4 x^{3}-4 c_{2} {\mathrm e}^{x}-4 c_{3} x -2 x^{2}-4 c_{1} \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 47
DSolve[y'''[x]-4*y''[x]+5*y'[x]-2*y[x]==3*x^2*Exp[x]-7*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^x \left (-x^4-4 x^3+2 x^2+4 (1+c_2) x+4 \left (c_3 e^x+1+c_1\right )\right ) \]