Internal problem ID [3090]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 342.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Abel]
Solve \begin {gather*} \boxed {\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 153
dsolve((b*x+a)^2*diff(y(x),x)+c*y(x)^2+(b*x+a)*y(x)^3 = 0,y(x), singsol=all)
\[ c_{1}+\left (x +\frac {a}{b}+\frac {c \sqrt {\pi }\, \sqrt {2}\, \erf \left (\frac {\sqrt {2}\, \left (b^{2} x +a b +c y \relax (x )\right )}{2 \sqrt {b}\, y \relax (x ) \left (b x +a \right )}\right ) {\mathrm e}^{\frac {\left (b^{2} x +a b +c y \relax (x )\right )^{2}}{2 y \relax (x )^{2} \left (b x +a \right )^{2} b}}}{2 b^{\frac {3}{2}}}\right ) {\mathrm e}^{-\frac {\left (b^{2} x +b x y \relax (x )+a b +a y \relax (x )+c y \relax (x )\right ) \left (b^{2} x -b x y \relax (x )+a b -a y \relax (x )+c y \relax (x )\right )}{2 y \relax (x )^{2} \left (b x +a \right )^{2} b}} = 0 \]
✓ Solution by Mathematica
Time used: 1.433 (sec). Leaf size: 149
DSolve[(a+b x)^2 y'[x]+c y[x]^2+(a+b x)y[x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {c}{\sqrt {-b (a+b x)^2}}=\frac {2 \exp \left (\frac {1}{2} \left (-\frac {c}{\sqrt {-b (a+b x)^2}}-\frac {\left (-b (a+b x)^2\right )^{3/2}}{b y(x) (a+b x)^3}\right )^2\right )}{\sqrt {2 \pi } \text {Erfi}\left (\frac {-\frac {c}{\sqrt {-b (a+b x)^2}}-\frac {\left (-b (a+b x)^2\right )^{3/2}}{b y(x) (a+b x)^3}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]