4.43.22 \(y'''(x)-2 y''(x)-3 y'(x)=3 x^2+\sin (x)\)

ODE
\[ y'''(x)-2 y''(x)-3 y'(x)=3 x^2+\sin (x) \] ODE Classification

[[_3rd_order, _missing_y]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.454822 (sec), leaf count = 58

\[\left \{\left \{y(x)\to \frac {1}{9} \left (-3 x^3+6 x^2-14 x-9 c_1 e^{-x}+3 c_2 e^{3 x}+9 c_3\right )+\frac {\sin (x)}{10}+\frac {\cos (x)}{5}\right \}\right \}\]

Maple ✓
cpu = 0.303 (sec), leaf count = 41

\[\left [y \left (x \right ) = -{\mathrm e}^{-x} \textit {\_C1} +\frac {{\mathrm e}^{3 x} \textit {\_C2}}{3}+\frac {2 x^{2}}{3}-\frac {x^{3}}{3}+\frac {\sin \left (x \right )}{10}+\frac {\cos \left (x \right )}{5}-\frac {14 x}{9}+\textit {\_C3}\right ]\] Mathematica raw input

DSolve[-3*y'[x] - 2*y''[x] + y'''[x] == 3*x^2 + Sin[x],y[x],x]

Mathematica raw output

{{y[x] -> (-14*x + 6*x^2 - 3*x^3 - (9*C[1])/E^x + 3*E^(3*x)*C[2] + 9*C[3])/9 + C
os[x]/5 + Sin[x]/10}}

Maple raw input

dsolve(diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-3*diff(y(x),x) = 3*x^2+sin(x), y(x))

Maple raw output

[y(x) = -exp(-x)*_C1+1/3*exp(3*x)*_C2+2/3*x^2-1/3*x^3+1/10*sin(x)+1/5*cos(x)-14/
9*x+_C3]