4.41.43 $\sqrt{y(x)}{y}^{″}(x)=2(a+bx)$

ODE
$$\sqrt{y(x)}{y}^{″}(x)=2(a+bx)$$ ODE Classification

[[_2nd_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✗
cpu = 0.388484 (sec), leaf count = 0 , could not solve

DSolve[Sqrt[y[x]]*Derivative[2][y][x] == 2*(a + b*x), y[x], x]

Maple ✓
cpu = 7.823 (sec), leaf count = 257

$$\{\ln (bx+a)-{\int }^{\frac{y\left(x\right)}{{(bx+a)}^2}}-b^2\sqrt{3}(\sqrt{3}(\sqrt[3]{-\frac{a+b}{\mathit{\_}\mathit{g}{b}^2}\frac{1}{\sqrt{\mathit{\_}\mathit{g}{(a+b)}^2}}}-2)+3\sqrt[3]{-\frac{a+b}{\sqrt{\mathit{\_}\mathit{g}{(a+b)}^2}\mathit{\_}\mathit{g}{b}^2}}\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(12b^2\int \frac{\sqrt{\mathit{\_}\mathit{g}{(a+b)}^2}}{\sqrt{\mathit{\_}\mathit{g}{(a+b)}^2}\mathit{\_}\mathit{g}{b}^2-a-b}{(-\frac{a+b}{\sqrt{\mathit{\_}\mathit{g}{(a+b)}^2}\mathit{\_}\mathit{g}{b}^2})}^{2/3}\mathrm{d}\mathit{\_}\mathit{g}-8\mathit{\_}\mathit{Z}\sqrt{3}-\ln \left(\mathit{\_}\mathit{g}{(a+b)}^2\right)+2\ln \left(\frac{{({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+1)}^2\sqrt{\mathit{\_}\mathit{g}{(a+b)}^2}}{{(\tan \left(\mathit{\_}\mathit{Z}\right))}^4+4\sqrt{3}{(\tan \left(\mathit{\_}\mathit{Z}\right))}^3+18{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2+12\tan \left(\mathit{\_}\mathit{Z}\right)\sqrt{3}+9}\right)+24\mathit{\_}\mathit{C}\mathit{1})\right))\sqrt{\mathit{\_}\mathit{g}{(a+b)}^2}{(-12\sqrt{\mathit{\_}\mathit{g}{(a+b)}^2}\mathit{\_}\mathit{g}{b}^2+12a+12b)}^{-1}d\mathit{\_}\mathit{g}-\mathit{\_}\mathit{C}\mathit{2}=0\}$$ Mathematica raw input

DSolve[Sqrt[y[x]]*y''[x] == 2*(a + b*x),y[x],x]

Mathematica raw output

DSolve[Sqrt[y[x]]*Derivative[2][y][x] == 2*(a + b*x), y[x], x]

Maple raw input

dsolve(diff(diff(y(x),x),x)*y(x)^(1/2) = 2*b*x+2*a, y(x),'implicit')

Maple raw output

ln(b*x+a)-Intat(-b^2*3^(1/2)*(3^(1/2)*((-(a+b)/(_g*(a+b)^2)^(1/2)/_g/b^2)^(1/3)-
2)+3*(-(a+b)/(_g*(a+b)^2)^(1/2)/_g/b^2)^(1/3)*tan(RootOf(12*b^2*Int((-(a+b)/(_g*
(a+b)^2)^(1/2)/_g/b^2)^(2/3)*(_g*(a+b)^2)^(1/2)/((_g*(a+b)^2)^(1/2)*_g*b^2-a-b),
_g)-8*_Z*3^(1/2)-ln(_g*(a+b)^2)+2*ln((tan(_Z)^2+1)^2*(_g*(a+b)^2)^(1/2)/(tan(_Z)
^4+4*3^(1/2)*tan(_Z)^3+18*tan(_Z)^2+12*tan(_Z)*3^(1/2)+9))+24*_C1)))*(_g*(a+b)^2
)^(1/2)/(-12*(_g*(a+b)^2)^(1/2)*_g*b^2+12*a+12*b),_g = y(x)/(b*x+a)^2)-_C2 = 0