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 = 0.260187 (sec), leaf count = 58

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

Maple ✓
cpu = 0.053 (sec), leaf count = 41

\[ \left \{ y \left ( x \right ) =-{{\rm e}^{-x}}{\it \_C2}+{\frac {{{\rm e}^{3\,x}}{\it \_C1}}{3}}-{\frac {{x}^{3}}{3}}+{\frac {\cos \left ( x \right ) }{5}}+{\frac {\sin \left ( x \right ) }{10}}+{\frac {2\,{x}^{2}}{3}}-{\frac {14\,x}{9}}+{\it \_C3} \right \} \] 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),'implicit')

Maple raw output

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