2.647   ODE No. 647

\[ y'(x)=\frac {x \left (a y(x)^2+b x^2\right )^2}{a^{5/2} y(x)} \]

✓ Mathematica : cpu = 0.298669 (sec), leaf count = 115

DSolve[Derivative[1][y][x] == (x*(b*x^2 + a*y[x]^2)^2)/(a^(5/2)*y[x]),y[x],x]
 

\[\left \{\left \{y(x)\to -\sqrt {-\frac {b x^2}{a}+\frac {\sqrt {b} \tan \left (\frac {a^{3/2} b x^2+2 c_1}{a^{9/4} \sqrt {b}}\right )}{\sqrt [4]{a}}}\right \},\left \{y(x)\to \sqrt {-\frac {b x^2}{a}+\frac {\sqrt {b} \tan \left (\frac {a^{3/2} b x^2+2 c_1}{a^{9/4} \sqrt {b}}\right )}{\sqrt [4]{a}}}\right \}\right \}\]

✓ Maple : cpu = 0.332 (sec), leaf count = 460

dsolve(diff(y(x),x) = (a*y(x)^2+b*x^2)^2*x/a^(5/2)/y(x),y(x))
 

\[y \left (x \right ) = \frac {\sqrt {-\left (c_{1} {\mathrm e}^{\frac {x^{2} \left (2 a^{{3}/{2}} \sqrt {-\frac {b}{a^{{3}/{2}}}}+b \,x^{2}\right )}{2 a^{{3}/{2}}}}+{\mathrm e}^{\frac {x^{2} \left (-2 a^{{3}/{2}} \sqrt {-\frac {b}{a^{{3}/{2}}}}+b \,x^{2}\right )}{2 a^{{3}/{2}}}}\right ) \left (\left (b \,x^{2}-a^{{3}/{2}} \sqrt {-\frac {b}{a^{{3}/{2}}}}\right ) {\mathrm e}^{\frac {x^{2} \left (-2 a^{{3}/{2}} \sqrt {-\frac {b}{a^{{3}/{2}}}}+b \,x^{2}\right )}{2 a^{{3}/{2}}}}+c_{1} \left (a^{{3}/{2}} \sqrt {-\frac {b}{a^{{3}/{2}}}}+b \,x^{2}\right ) {\mathrm e}^{\frac {x^{2} \left (2 a^{{3}/{2}} \sqrt {-\frac {b}{a^{{3}/{2}}}}+b \,x^{2}\right )}{2 a^{{3}/{2}}}}\right ) a}}{a \left (c_{1} {\mathrm e}^{\frac {x^{2} \left (2 a^{{3}/{2}} \sqrt {-\frac {b}{a^{{3}/{2}}}}+b \,x^{2}\right )}{2 a^{{3}/{2}}}}+{\mathrm e}^{\frac {x^{2} \left (-2 a^{{3}/{2}} \sqrt {-\frac {b}{a^{{3}/{2}}}}+b \,x^{2}\right )}{2 a^{{3}/{2}}}}\right )}\]