Internal problem ID [10254]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 50. Method of
undetermined coefficients. Page 107
Problem number: Ex 6.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }-3 x^{2}-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)-3*diff(y(x),x)=3*x^2+sin(x),y(x), singsol=all)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-x}+\frac {{\mathrm e}^{3 x} c_{2}}{3}+\frac {2 x^{2}}{3}-\frac {x^{3}}{3}+\frac {\sin \relax (x )}{10}+\frac {\cos \relax (x )}{5}-\frac {14 x}{9}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.163 (sec). Leaf size: 53
DSolve[y'''[x]-2*y''[x]-3*y'[x]==3*x^2+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{9} x (3 (x-2) x+14)+\frac {\sin (x)}{10}+\frac {\cos (x)}{5}-c_1 e^{-x}+\frac {1}{3} c_2 e^{3 x}+c_3 \\ \end{align*}