#### 2.169   ODE No. 169

$(a x+b)^2 y'(x)+y(x)^3 (a x+b)+c y(x)^2=0$ Mathematica : cpu = 1.89509 (sec), leaf count = 149

$\text {Solve}\left [-\frac {c}{\sqrt {-a (a x+b)^2}}=\frac {2 \exp \left (\frac {1}{2} \left (-\frac {c}{\sqrt {-a (a x+b)^2}}-\frac {\left (-a (a x+b)^2\right )^{3/2}}{a y(x) (a x+b)^3}\right )^2\right )}{\sqrt {2 \pi } \text {erfi}\left (\frac {-\frac {c}{\sqrt {-a (a x+b)^2}}-\frac {\left (-a (a x+b)^2\right )^{3/2}}{a y(x) (a x+b)^3}}{\sqrt {2}}\right )+2 c_1},y(x)\right ]$ Maple : cpu = 0.119 (sec), leaf count = 153

$\left \{ {\frac {1}{2} \left ( \left ( \sqrt {2}\sqrt {\pi }{\it Erf} \left ( {\frac {\sqrt {2} \left ( cy \left ( x \right ) +a \left ( ax+b \right ) \right ) }{2\, \left ( ax+b \right ) y \left ( x \right ) }{\frac {1}{\sqrt {a}}}} \right ) {{\rm e}^{{\frac { \left ( cy \left ( x \right ) +a \left ( ax+b \right ) \right ) ^{2}}{2\, \left ( y \left ( x \right ) \right ) ^{2} \left ( ax+b \right ) ^{2}a}}}}ac+2\, \left ( ax+b \right ) {a}^{3/2} \right ) {{\rm e}^{-{\frac { \left ( \left ( ax+b+c \right ) y \left ( x \right ) +a \left ( ax+b \right ) \right ) \left ( \left ( -ax-b+c \right ) y \left ( x \right ) +a \left ( ax+b \right ) \right ) }{2\, \left ( y \left ( x \right ) \right ) ^{2} \left ( ax+b \right ) ^{2}a}}}}+2\,{\it \_C1}\,{a}^{5/2} \right ) {a}^{-{\frac {5}{2}}}}=0 \right \}$