2.1774   ODE No. 1774

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

$$a{x}^{2}y(x)y^{″}(x)+b{x}^2{y}^{\prime }(x{)}^2+cxy(x)y^{\prime }(x)+dy(x{)}^2=0$$ ✓ Mathematica : cpu = 1.31436 (sec), leaf count = 93

$$\left\{\{y(x)\to c_2\exp (-\frac{\log (x)(a\sqrt{\frac{a^2-2ac-4ad-4bd+c^2}{a^2}}-a+c)-2a\log (x^{\sqrt{\frac{a^2-2ac-4ad-4bd+c^2}{a^2}}}+c_1)}{2(a+b)})\}\right\}$$

✓ Maple : cpu = 0.508 (sec), leaf count = 155

$$\{y\left(x\right)=x^{-\frac{1}{2a+2b}\sqrt{a^2-2ac-4da-4db+c^2}}{x}^{\frac{a}{2a+2b}}{x}^{-\frac{c}{2a+2b}}{\left((a^2-2ac-4da-4db+c^2){(x^{\frac{1}{a}\sqrt{a^2-2ac-4da-4db+c^2}}\mathit{\_}\mathit{C}\mathit{1}a+x^{\frac{1}{a}\sqrt{a^2-2ac-4da-4db+c^2}}\mathit{\_}\mathit{C}\mathit{1}b-\mathit{\_}\mathit{C}\mathit{2}a-\mathit{\_}\mathit{C}\mathit{2}b)}^{-2}\right)}^{-\frac{a}{2a+2b}}\}$$