29.12.23 problem 342

Internal problem ID [4942]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 342
Date solved : Sunday, March 30, 2025 at 04:17:22 AM
CAS classification : [_rational, _Abel]

\begin{align*} \left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3}&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 153

ode:=(b*x+a)^2*diff(y(x),x)+c*y(x)^2+(b*x+a)*y(x)^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {\left (\operatorname {erf}\left (\frac {\left (c y+b \left (b x +a \right )\right ) \sqrt {2}}{2 \sqrt {b}\, y \left (b x +a \right )}\right ) {\mathrm e}^{\frac {\left (c y+b \left (b x +a \right )\right )^{2}}{2 y^{2} \left (b x +a \right )^{2} b}} \sqrt {\pi }\, \sqrt {2}\, b c +2 b^{{3}/{2}} \left (b x +a \right )\right ) {\mathrm e}^{-\frac {\left (\left (-b x -a +c \right ) y+b \left (b x +a \right )\right ) \left (\left (b x +a +c \right ) y+b \left (b x +a \right )\right )}{2 y^{2} \left (b x +a \right )^{2} b}}+2 c_1 \,b^{{5}/{2}}}{2 b^{{5}/{2}}} = 0 \]

✓ Mathematica. Time used: 1.329 (sec). Leaf size: 149

ode=(a+b x)^2 D[y[x],x]+c y[x]^2+(a+b x)y[x]^3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [-\frac {c}{\sqrt {-b (a+b x)^2}}=\frac {2 \exp \left (\frac {1}{2} \left (-\frac {c}{\sqrt {-b (a+b x)^2}}-\frac {\left (-b (a+b x)^2\right )^{3/2}}{b y(x) (a+b x)^3}\right )^2\right )}{\sqrt {2 \pi } \text {erfi}\left (\frac {-\frac {c}{\sqrt {-b (a+b x)^2}}-\frac {\left (-b (a+b x)^2\right )^{3/2}}{b y(x) (a+b x)^3}}{\sqrt {2}}\right )+2 c_1},y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(c*y(x)**2 + (a + b*x)**2*Derivative(y(x), x) + (a + b*x)*y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out