ODE No. 169

$$(ax+b{)}^2{y}^{\prime }(x)+y(x{)}^3(ax+b)+cy(x{)}^2=0$$ ✓ Mathematica : cpu = 2.11208 (sec), leaf count = 149

DSolve[c*y[x]^2 + (b + a*x)*y[x]^3 + (b + a*x)^2*Derivative[1][y][x] == 0,y[x],x]
 

$$\text{Solve}[-\frac{c}{\sqrt{-a(ax+b{)}^2}}=\frac{2\exp \left(\frac{1}{2}{(-\frac{c}{\sqrt{-a(ax+b{)}^2}}-\frac{{(-a(ax+b{)}^2)}^{3/2}}{ay(x)(ax+b{)}^3})}^2\right)}{\sqrt{2\pi }\text{erfi}\left(\frac{-\frac{c}{\sqrt{-a(ax+b{)}^2}}-\frac{{(-a(ax+b{)}^2)}^{3/2}}{ay(x)(ax+b{)}^3}}{\sqrt{2}}\right)+2c_1},y(x)]$$ ✓ Maple : cpu = 0.136 (sec), leaf count = 153

dsolve((a*x+b)^2*diff(y(x),x)+(a*x+b)*y(x)^3+c*y(x)^2 = 0,y(x))
 

$$\frac{(\sqrt{\pi }\sqrt{2}\mathrm{erf}\left(\frac{\sqrt{2}(cy\left(x\right)+a(ax+b))}{2\sqrt{a}y\left(x\right)(ax+b)}\right){\mathrm{e}}^{\frac{{(cy\left(x\right)+a(ax+b))}^2}{2y{\left(x\right)}^2{(ax+b)}^{2}a}}ac+2(ax+b)a^{\frac{3}{2}}){\mathrm{e}}^{-\frac{((-ax-b+c)y\left(x\right)+a(ax+b))((ax+b+c)y\left(x\right)+a(ax+b))}{2y{\left(x\right)}^2{(ax+b)}^{2}a}}+2c_1{a}^{\frac{5}{2}}}{2a^{\frac{5}{2}}}=0$$