4.45.3 $x^4{y}^{‴}(x)+2x^3{y}^{″}(x)+2xy(x)=10(x^2+1)$

ODE
$$x^4{y}^{‴}(x)+2x^3{y}^{″}(x)+2xy(x)=10(x^2+1)$$ ODE Classification

[[_3rd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0605516 (sec), leaf count = 42

$$\left\{\{y(x)\to \frac{5c_3+25x^2+10\log (x)+8}{5x}+c_{1}x\sin (\log (x))+c_{2}x\cos (\log (x))\}\right\}$$

Maple ✓
cpu = 0.161 (sec), leaf count = 143

$$\{y\left(x\right)=\frac{1}{5x}(((5\mathit{\_}\mathit{C}\mathit{2}{x}^2-8)\cos (\ln \left(x\right))+5\mathit{\_}\mathit{C}\mathit{3}{x}^2\sin (\ln \left(x\right))+5x^2+5\mathit{\_}\mathit{C}\mathit{1}+10\ln \left(x\right)+6\sin (\ln \left(x\right))){(\tan \left(\frac{\ln \left(x\right)}{2}\right))}^2+(-20x^2\cos (\ln \left(x\right))+40x^2\sin (\ln \left(x\right))+12\cos (\ln \left(x\right))+16\sin (\ln \left(x\right)))\tan \left(\frac{\ln \left(x\right)}{2}\right)+(8+(5\mathit{\_}\mathit{C}\mathit{2}+40)x^2)\cos (\ln \left(x\right))+(-6+(5\mathit{\_}\mathit{C}\mathit{3}+20)x^2)\sin (\ln \left(x\right))+5x^2+5\mathit{\_}\mathit{C}\mathit{1}+10\ln \left(x\right)){(1+{(\tan \left(\frac{\ln \left(x\right)}{2}\right))}^2)}^{-1}\}$$ Mathematica raw input

DSolve[2*x*y[x] + 2*x^3*y''[x] + x^4*y'''[x] == 10*(1 + x^2),y[x],x]

Mathematica raw output

{{y[x] -> x*C[2]*Cos[Log[x]] + (8 + 25*x^2 + 5*C[3] + 10*Log[x])/(5*x) + x*C[1]*
Sin[Log[x]]}}

Maple raw input

dsolve(x^4*diff(diff(diff(y(x),x),x),x)+2*x^3*diff(diff(y(x),x),x)+2*x*y(x) = 10*x^2+10, y(x),'implicit')

Maple raw output

y(x) = 1/5*(((5*_C2*x^2-8)*cos(ln(x))+5*_C3*x^2*sin(ln(x))+5*x^2+5*_C1+10*ln(x)+
6*sin(ln(x)))*tan(1/2*ln(x))^2+(-20*x^2*cos(ln(x))+40*x^2*sin(ln(x))+12*cos(ln(x
))+16*sin(ln(x)))*tan(1/2*ln(x))+(8+(5*_C2+40)*x^2)*cos(ln(x))+(-6+(5*_C3+20)*x^
2)*sin(ln(x))+5*x^2+5*_C1+10*ln(x))/(1+tan(1/2*ln(x))^2)/x