4.45.5 $(x^2+1)x^2{y}^{‴}(x)+8x^3{y}^{″}(x)+10x^2{y}^{\prime }(x)=3x^2+2x^2\log (x)-1$

ODE
$$(x^2+1)x^2{y}^{‴}(x)+8x^3{y}^{″}(x)+10x^2{y}^{\prime }(x)=3x^2+2x^2\log (x)-1$$ ODE Classification

[[_3rd_order, _missing_y]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.115352 (sec), leaf count = 62

$$\left\{\{y(x)\to c_3-\frac{100(3c_2-1)x^3+900c_{2}x+225c_1+36x^5-60(3x^4+10x^2+15)x\log (x)}{900{(x^2+1)}^2}\}\right\}$$

Maple ✓
cpu = 0.18 (sec), leaf count = 67

$$\{y\left(x\right)=\frac{(180x^5+600x^3+900x)\ln \left(x\right)-36x^5+900\mathit{\_}\mathit{C}\mathit{3}{x}^4+(-900\mathit{\_}\mathit{C}\mathit{1}+100)x^3+1800\mathit{\_}\mathit{C}\mathit{3}{x}^2-2700\mathit{\_}\mathit{C}\mathit{1}x-225\mathit{\_}\mathit{C}\mathit{2}+900\mathit{\_}\mathit{C}\mathit{3}}{900{(x^2+1)}^2}\}$$ Mathematica raw input

DSolve[10*x^2*y'[x] + 8*x^3*y''[x] + x^2*(1 + x^2)*y'''[x] == -1 + 3*x^2 + 2*x^2*Log[x],y[x],x]

Mathematica raw output

{{y[x] -> C[3] - (36*x^5 + 225*C[1] + 900*x*C[2] + 100*x^3*(-1 + 3*C[2]) - 60*x*
(15 + 10*x^2 + 3*x^4)*Log[x])/(900*(1 + x^2)^2)}}

Maple raw input

dsolve(x^2*(x^2+1)*diff(diff(diff(y(x),x),x),x)+8*x^3*diff(diff(y(x),x),x)+10*x^2*diff(y(x),x) = 2*x^2*ln(x)-1+3*x^2, y(x),'implicit')

Maple raw output

y(x) = 1/900*((180*x^5+600*x^3+900*x)*ln(x)-36*x^5+900*_C3*x^4+(-900*_C1+100)*x^
3+1800*_C3*x^2-2700*_C1*x-225*_C2+900*_C3)/(x^2+1)^2