2.368   ODE No. 368

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

$$ay(x)+b{x}^2+y^{\prime }(x{)}^2=0$$ ✓ Mathematica : cpu = 1.37749 (sec), leaf count = 795

$$\{\text{Solve}[{\int }_1^x(\frac{2\sqrt{-bK[1{]}^2-ay(x)}y(x)}{bK[1{]}^4+ay(x)K[1{]}^2+4y(x{)}^2}+\frac{bK[1{]}^3+ay(x)K[1]}{bK[1{]}^4+ay(x)K[1{]}^2+4y(x{)}^2})dK[1]+{\int }_1^{y(x)}(-\frac{\sqrt{-b{x}^2-aK[2]}x}{b{x}^4+aK[2]x^2+4K[2{]}^2}-{\int }_1^x(\frac{aK[1]}{bK[1{]}^4+aK[2]K[1{]}^2+4K[2{]}^2}+\frac{2\sqrt{-bK[1{]}^2-aK[2]}}{bK[1{]}^4+aK[2]K[1{]}^2+4K[2{]}^2}-\frac{aK[2]}{\sqrt{-bK[1{]}^2-aK[2]}(bK[1{]}^4+aK[2]K[1{]}^2+4K[2{]}^2)}-\frac{(aK[1{]}^2+8K[2])(bK[1{]}^3+aK[2]K[1])}{{(bK[1{]}^4+aK[2]K[1{]}^2+4K[2{]}^2)}^2}-\frac{2K[2](aK[1{]}^2+8K[2])\sqrt{-bK[1{]}^2-aK[2]}}{{(bK[1{]}^4+aK[2]K[1{]}^2+4K[2{]}^2)}^2})dK[1]+\frac{2K[2]}{b{x}^4+aK[2]x^2+4K[2{]}^2})dK[2]=c_1,y(x)],\text{Solve}[{\int }_1^x(\frac{bK[3{]}^3+ay(x)K[3]}{bK[3{]}^4+ay(x)K[3{]}^2+4y(x{)}^2}-\frac{2y(x)\sqrt{-bK[3{]}^2-ay(x)}}{bK[3{]}^4+ay(x)K[3{]}^2+4y(x{)}^2})dK[3]+{\int }_1^{y(x)}(\frac{\sqrt{-b{x}^2-aK[4]}x}{b{x}^4+aK[4]x^2+4K[4{]}^2}-{\int }_1^x(\frac{aK[3]}{bK[3{]}^4+aK[4]K[3{]}^2+4K[4{]}^2}-\frac{2\sqrt{-bK[3{]}^2-aK[4]}}{bK[3{]}^4+aK[4]K[3{]}^2+4K[4{]}^2}+\frac{aK[4]}{\sqrt{-bK[3{]}^2-aK[4]}(bK[3{]}^4+aK[4]K[3{]}^2+4K[4{]}^2)}-\frac{(aK[3{]}^2+8K[4])(bK[3{]}^3+aK[4]K[3])}{{(bK[3{]}^4+aK[4]K[3{]}^2+4K[4{]}^2)}^2}+\frac{2K[4](aK[3{]}^2+8K[4])\sqrt{-bK[3{]}^2-aK[4]}}{{(bK[3{]}^4+aK[4]K[3{]}^2+4K[4{]}^2)}^2})dK[3]+\frac{2K[4]}{b{x}^4+aK[4]x^2+4K[4{]}^2})dK[4]=c_1,y(x)]\}$$ ✗ Maple : cpu = 0. (sec), leaf count = 0 , exception

time expired