2.1755   ODE No. 1755

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

$$ay(x)y^{″}(x)+b{y}^{\prime }(x{)}^2+\text{c0}+\text{c1}y(x)+\text{c2}y(x{)}^2+\text{c3}y(x{)}^3+\text{c4}y(x{)}^4=0$$ ✗ Mathematica : cpu = 104.055 (sec), leaf count = 0 , could not solve

DSolve[c0 + c1*y[x] + c2*y[x]^2 + c3*y[x]^3 + c4*y[x]^4 + b*Derivative[1][y][x]^2 + a*y[x]*Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.341 (sec), leaf count = 418

$$\{{\int }^{y\left(x\right)}(2a+b)(3a+2b)(a+b)(a+2b)b{\mathit{\_}\mathit{a}}^{2\frac{b}{a}}\frac{1}{\sqrt{-36(a+2/3b)b(a+b)(a+b/2){\mathit{\_}\mathit{a}}^{2\frac{b}{a}}(a+2b)(2/3b(a+b)\mathit{c}\mathit{3}(a+b/2)(a+2b){\mathit{\_}\mathit{a}}^{\frac{3a+2b}{a}}+(a+2/3b)(b\mathit{c}\mathit{2}(a+b/2)(a+2b){\mathit{\_}\mathit{a}}^{\frac{2b+2a}{a}}+(1/2b\mathit{c}\mathit{4}(a+2b){\mathit{\_}\mathit{a}}^{\frac{2b+4a}{a}}+(a+b/2)(2{\mathit{\_}\mathit{a}}^{\frac{a+2b}{a}}b\mathit{c}\mathit{1}+({\mathit{\_}\mathit{a}}^{2\frac{b}{a}}\mathit{c}\mathit{0}-\mathit{\_}\mathit{C}\mathit{1}b)(a+2b)))(a+b)))}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-6(a+2/3b)b(a+b)(a+b/2)(a+2b){\mathit{\_}\mathit{a}}^{2\frac{b}{a}}\frac{1}{\sqrt{-36(a+2/3b)b(a+b)(a+b/2){\mathit{\_}\mathit{a}}^{2\frac{b}{a}}(a+2b)(2/3b(a+b)\mathit{c}\mathit{3}(a+b/2)(a+2b){\mathit{\_}\mathit{a}}^{\frac{3a+2b}{a}}+(a+2/3b)(b\mathit{c}\mathit{2}(a+b/2)(a+2b){\mathit{\_}\mathit{a}}^{\frac{2b+2a}{a}}+(1/2b\mathit{c}\mathit{4}(a+2b){\mathit{\_}\mathit{a}}^{\frac{2b+4a}{a}}+(a+b/2)(2{\mathit{\_}\mathit{a}}^{\frac{a+2b}{a}}b\mathit{c}\mathit{1}+({\mathit{\_}\mathit{a}}^{2\frac{b}{a}}\mathit{c}\mathit{0}-\mathit{\_}\mathit{C}\mathit{1}b)(a+2b)))(a+b)))}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$