Internal problem ID [11814]
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: 40.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-6 y^{\prime \prime }+9 y^{\prime }-4 y=8 x^{2}+3-6 \,{\mathrm e}^{2 x}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 7, y^{\prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve([diff(y(x),x$3)-6*diff(y(x),x$2)+9*diff(y(x),x)-4*y(x)=8*x^2+3-6*exp(2*x),y(0) = 1, D(y)(0) = 7, (D@@2)(y)(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = -2 x^{2}-9 x +3 \,{\mathrm e}^{2 x}-15+\frac {44 \,{\mathrm e}^{x}}{3}-\frac {5 \,{\mathrm e}^{4 x}}{3}+2 \,{\mathrm e}^{x} x \]
✓ Solution by Mathematica
Time used: 0.21 (sec). Leaf size: 42
DSolve[{y'''[x]-6*y''[x]+9*y'[x]-4*y[x]==8*x^2+3-6*Exp[2*x],{y[0]==1,y'[0]==7,y''[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 x^2-9 x+3 e^{2 x}-\frac {5 e^{4 x}}{3}+e^x \left (2 x+\frac {44}{3}\right )-15 \]