ODE No. 1691

8.101 ODE No. 1691

${(a x^{2} + b x + c)}^{3 / 2} \frac{d^{2}}{d x^{2}} y (x) - F (\frac{y (x)}{\sqrt{a x^{2} + b x + c}}) = 0$

Mathematica: cpu = 61.997373 (sec), leaf count = 46 $DSolve [y^{″} (x) {(a x^{2} + b x + c)}^{3 / 2} - f (\frac{y (x)}{\sqrt{a x^{2} + b x + c}}) = 0, y (x), x]$

Maple: cpu = 0.795 (sec), leaf count = 254 ${y (x) = R o o t O f (- 2 a \arctan (\frac{2 a x + b}{\sqrt{4 a c - b^{2}}}) - 2 \int^{_Z} \frac{a}{\sqrt{4_C 1 a^{2} - 4 c {_g}^{2} a + b^{2} {_g}^{2} + 8 \int F (_g) d_g}} d_g \sqrt{4 a c - b^{2}} +_C 2 \sqrt{4 a c - b^{2}}) \sqrt{a x^{2} + b x + c}, y (x) = R o o t O f (- 2 a \arctan (\frac{2 a x + b}{\sqrt{4 a c - b^{2}}}) + 2 \int^{_Z} \frac{a}{\sqrt{4_C 1 a^{2} - 4 c {_g}^{2} a + b^{2} {_g}^{2} + 8 \int F (_g) d_g}} d_g \sqrt{4 a c - b^{2}} +_C 2 \sqrt{4 a c - b^{2}}) \sqrt{a x^{2} + b x + c}, y (x) = R o o t O f (4_Z a c -_Z b^{2} - 4 F (\frac{_Z}{\sqrt{a x^{2} + b x + c}}) \sqrt{a x^{2} + b x + c})}$

[next] [prev] [prev-tail] [front] [up]