Internal problem ID [11268]
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]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }-3 y^{\prime }=3 x^{2}+\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = -\frac {x^{3}}{3}+\frac {2 x^{2}}{3}-c_{1} {\mathrm e}^{-x}+\frac {c_{2} {\mathrm e}^{3 x}}{3}+\frac {\sin \left (x \right )}{10}+\frac {\cos \left (x \right )}{5}-\frac {14 x}{9}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.68 (sec). Leaf size: 58
DSolve[y'''[x]-2*y''[x]-3*y'[x]==3*x^2+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{9} \left (-3 x^3+6 x^2-14 x-9 c_1 e^{-x}+3 c_2 e^{3 x}+9 c_3\right )+\frac {\sin (x)}{10}+\frac {\cos (x)}{5} \]