2.532   ODE No. 532

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

$$a{y}^{\prime }(x{)}^3+b{y}^{\prime }(x{)}^2+c{y}^{\prime }(x)-d-y(x)=0$$ ✗ Mathematica : cpu = 300.023 (sec), leaf count = 0 , timed out

$Aborted

✓ Maple : cpu = 0.161 (sec), leaf count = 1208

$$\{x-{\int }^{y\left(x\right)}6\frac{a\sqrt[3]{108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3}}{{(108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3)}^{2/3}-2b\sqrt[3]{108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3}-12ca+4b^2}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}12\frac{a\sqrt[3]{108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3}}{(i\sqrt{3}-1)(i\sqrt[3]{108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3}\sqrt{3}b-6i\sqrt{3}ac+2i\sqrt{3}{b}^2+{(108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3)}^{2/3}+b\sqrt[3]{108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3}+6ca-2b^2)}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}-12\frac{a\sqrt[3]{108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3}}{(i\sqrt{3}+1)(-i\sqrt[3]{108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3}\sqrt{3}b+6i\sqrt{3}ac-2i\sqrt{3}{b}^2+{(108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3)}^{2/3}+b\sqrt[3]{108a^2\mathit{\_}\mathit{a}+12\sqrt{3}\sqrt{27{\mathit{\_}\mathit{a}}^2{a}^2+54\mathit{\_}\mathit{a}{a}^{2}d+18\mathit{\_}\mathit{a}abc-4\mathit{\_}\mathit{a}{b}^3+27a^2{d}^2+18abcd+4a{c}^3-4b^{3}d-b^2{c}^2}a+108a^{2}d+36bca-8b^3}+6ca-2b^2)}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0\}$$