2.368   ODE No. 368

\[ a y(x)+b x^2+y'(x)^2=0 \]

✓ Mathematica : cpu = 0.815559 (sec), leaf count = 581

DSolve[b*x^2 + a*y[x] + Derivative[1][y][x]^2 == 0,y[x],x]
 

\[\left \{\text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4-\text {$\#$1}^3 a+2 \text {$\#$1}^2 b+\text {$\#$1} a b+b^2\& ,\frac {2 \text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )-2 \text {$\#$1}^3 \log (x)-\text {$\#$1}^2 a \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+\text {$\#$1}^2 a \log (x)+2 \text {$\#$1} b \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+a b \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )-2 \text {$\#$1} b \log (x)-a b \log (x)}{4 \text {$\#$1}^3-3 \text {$\#$1}^2 a+4 \text {$\#$1} b+a b}\& \right ]-\log \left (\sqrt {-a y(x)} \sqrt {-a y(x)-b x^2}+a y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)=c_1,y(x)\right ],\text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4+\text {$\#$1}^3 a+2 \text {$\#$1}^2 b-\text {$\#$1} a b+b^2\& ,\frac {-2 \text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+2 \text {$\#$1}^3 \log (x)-\text {$\#$1}^2 a \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+\text {$\#$1}^2 a \log (x)-2 \text {$\#$1} b \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+a b \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+2 \text {$\#$1} b \log (x)-a b \log (x)}{-4 \text {$\#$1}^3-3 \text {$\#$1}^2 a-4 \text {$\#$1} b+a b}\& \right ]-\log \left (\sqrt {-a y(x)} \sqrt {-a y(x)-b x^2}+a y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)=c_1,y(x)\right ]\right \}\]

✗ Maple : cpu = 0. (sec), leaf count = 0

dsolve(diff(y(x),x)^2+a*y(x)+b*x^2 = 0,y(x))
 

, exception

time expired