Internal problem ID [11786]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y=3 x^{3}-8 x} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \left (c_{2} {\mathrm e}^{\frac {3 x}{2}}+c_{3} {\mathrm e}^{\frac {5 x}{2}}+\left (x^{3}+5 x^{2}+22 x +42\right ) {\mathrm e}^{x}+c_{1} \right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 46
DSolve[4*y'''[x]-4*y''[x]-5*y'[x]+3*y[x]==3*x^3-8*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3+5 x^2+22 x+c_1 e^{x/2}+c_2 e^{3 x/2}+c_3 e^{-x}+42 \]