ODE No. 1264

\[ \left (x^2+3 x+4\right ) y''(x)+\left (x^2+x+1\right ) y'(x)+(-2 x-3) y(x)=0 \]

✓ Mathematica : cpu = 0.0625556 (sec), leaf count = 23

DSolve[(-3 - 2*x)*y[x] + (1 + x + x^2)*Derivative[1][y][x] + (4 + 3*x + x^2)*Derivative[2][y][x] == 0,y[x],x]

\[\left \{\left \{y(x)\to c_2 \left (x^2+x+3\right )+c_1 e^{-x}\right \}\right \}\]

✓ Maple : cpu = 0.047 (sec), leaf count = 19

dsolve((x^2+3*x+4)*diff(diff(y(x),x),x)+(x^2+x+1)*diff(y(x),x)-(2*x+3)*y(x)=0,y(x))

\[y \left (x \right ) = c_{1} {\mathrm e}^{-x}+c_{2} \left (x^{2}+x +3\right )\]