ODE
\[ \sqrt {y(x)} y''(x)=2 (a+b x) \] 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
\[ \left \{ \ln \left ( bx+a \right ) -\int ^{{\frac {y \left ( x \right ) }{ \left ( bx+a \right ) ^{2}}}}\!-{{b}^{2}\sqrt {3} \left ( \sqrt {3} \left ( \sqrt [3]{-{\frac {a+b}{{\it \_g}\,{b}^{2}}{\frac {1}{\sqrt {{\it \_g}\, \left ( a+b \right ) ^{2}}}}}}-2 \right ) +3\,\sqrt [3]{-{\frac {a+b}{\sqrt {{\it \_g}\, \left ( a+b \right ) ^{2}}{\it \_g}\,{b}^{2}}}}\tan \left ( {\it RootOf} \left ( 12\,{b}^{2}\int \!{\frac {\sqrt {{\it \_g}\, \left ( a+b \right ) ^{2}}}{\sqrt {{\it \_g}\, \left ( a+b \right ) ^{2}}{\it \_g}\,{b}^{2}-a-b} \left ( -{\frac {a+b}{\sqrt {{\it \_g}\, \left ( a+b \right ) ^{2}}{\it \_g}\,{b}^{2}}} \right ) ^{2/3}}\,{\rm d}{\it \_g}-8\,{\it \_Z}\,\sqrt {3}-\ln \left ( {\it \_g}\, \left ( a+b \right ) ^{2} \right ) +2\,\ln \left ( {\frac { \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) ^{2}\sqrt {{\it \_g}\, \left ( a+b \right ) ^{2}}}{ \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{4}+4\,\sqrt {3} \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{3}+18\, \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+12\,\tan \left ( {\it \_Z} \right ) \sqrt {3}+9}} \right ) +24\,{\it \_C1} \right ) \right ) \right ) \sqrt {{\it \_g}\, \left ( a+b \right ) ^{2}} \left ( -12\,\sqrt {{\it \_g}\, \left ( a+b \right ) ^{2}}{\it \_g}\,{b}^{2}+12\,a+12\,b \right ) ^{-1}}{d{\it \_g}}-{\it \_C2}=0 \right \} \] 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