2.384   ODE No. 384

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ (\text {Global$\grave { }$a} \text {Global$\grave { }$x}+\text {Global$\grave { }$b}) \text {Global$\grave { }$y}'(\text {Global$\grave { }$x})-\text {Global$\grave { }$a} \text {Global$\grave { }$y}(\text {Global$\grave { }$x})+\text {Global$\grave { }$c}+\text {Global$\grave { }$y}'(\text {Global$\grave { }$x})^2=0 \] Mathematica : cpu = 2.05896 (sec), leaf count = 183

\[\left \{\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {-2 \sqrt {-e^{2 c_1} \text {Global$\grave { }$a}^4 \text {Global$\grave { }$x}^2-2 e^{2 c_1} \text {Global$\grave { }$a}^4 \text {Global$\grave { }$x}-e^{2 c_1} \text {Global$\grave { }$a}^4}-e^{2 c_1} \text {Global$\grave { }$a}+2 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$x}+\text {Global$\grave { }$a}^3-2 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}-\text {Global$\grave { }$a} \text {Global$\grave { }$b}^2+4 \text {Global$\grave { }$a} \text {Global$\grave { }$c}}{4 \text {Global$\grave { }$a}^2}\right \},\left \{\text {Global$\grave { }$y}(\text {Global$\grave { }$x})\to \frac {2 \sqrt {-e^{2 c_1} \text {Global$\grave { }$a}^4 \text {Global$\grave { }$x}^2-2 e^{2 c_1} \text {Global$\grave { }$a}^4 \text {Global$\grave { }$x}-e^{2 c_1} \text {Global$\grave { }$a}^4}-e^{2 c_1} \text {Global$\grave { }$a}+2 \text {Global$\grave { }$a}^3 \text {Global$\grave { }$x}+\text {Global$\grave { }$a}^3-2 \text {Global$\grave { }$a}^2 \text {Global$\grave { }$b} \text {Global$\grave { }$x}-\text {Global$\grave { }$a} \text {Global$\grave { }$b}^2+4 \text {Global$\grave { }$a} \text {Global$\grave { }$c}}{4 \text {Global$\grave { }$a}^2}\right \}\right \}\]

Maple : cpu = 0.025 (sec), leaf count = 50

\[ \left \{ y \left ( x \right ) ={\frac {-{a}^{2}{x}^{2}-2\,abx-{b}^{2}+4\,c}{4\,a}},y \left ( x \right ) ={\it \_C1}\,x+{\frac {{{\it \_C1}}^{2}+{\it \_C1}\,b+c}{a}} \right \} \]