ODE No. 1254

$$(x^2+x-2)y^{″}(x)+(x^2-x)y^{\prime }(x)+(-6x^2-7x)y(x)=0$$ ✓ Mathematica : cpu = 0.132401 (sec), leaf count = 69

DSolve[(-7*x - 6*x^2)*y[x] + (-x + x^2)*Derivative[1][y][x] + (-2 + x + x^2)*Derivative[2][y][x] == 0,y[x],x]
 

$$\left\{\{y(x)\to \frac{1}{5}{c}_2{e}^{-3x-5}(195e^{5x}x\text{Ei}(5-5x)-195e^{5x}\text{Ei}(5-5x)+e^{5}x+44e^5)-c_1{e}^{2x}(x-1)\}\right\}$$ ✓ Maple : cpu = 0.062 (sec), leaf count = 43

dsolve((x^2+x-2)*diff(diff(y(x),x),x)+(x^2-x)*diff(y(x),x)-(6*x^2+7*x)*y(x)=0,y(x))
 

$$y\left(x\right)=195c_2{\mathrm{e}}^{-5+2x}(x-1)\mathrm{expIntegral}(1,5x-5)-c_2(x+44){\mathrm{e}}^{-3x}+c_1{\mathrm{e}}^{2x}(x-1)$$