23.2.195 problem 200

Internal problem ID [5550]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 200
Date solved : Tuesday, September 30, 2025 at 12:52:34 PM
CAS classification : [[_homogeneous, `class C`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.241 (sec). Leaf size: 149

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

\begin{align*} y &= -\frac {-2 b x +a}{2 \sqrt {-b}} \\ y &= \frac {-2 b x +a}{2 \sqrt {-b}} \\ y &= 0 \\ y &= \sqrt {\frac {c_1 b +\sqrt {c_1 b \left (-2 b x +a \right )^{2}}}{b}} \\ y &= \sqrt {-\frac {-c_1 b +\sqrt {c_1 b \left (-2 b x +a \right )^{2}}}{b}} \\ y &= -\sqrt {\frac {c_1 b +\sqrt {c_1 b \left (-2 b x +a \right )^{2}}}{b}} \\ y &= -\sqrt {\frac {c_1 b -\sqrt {c_1 b \left (-2 b x +a \right )^{2}}}{b}} \\ \end{align*}

✓ Mathematica. Time used: 0.656 (sec). Leaf size: 409

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

\begin{align*} \text {Solve}\left [\frac {\left (b-\sqrt {b^2}\right ) \log (y(x))}{b}-\frac {-b \log \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}-a-2 \sqrt {b^2} x\right )+\sqrt {b^2} \log \left (b \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}-a-2 \sqrt {b^2} x\right )\right )-\left (\sqrt {b^2}+b\right ) \log \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}+a-2 \sqrt {b^2} x\right )}{2 \sqrt {b^2}}=c_1,y(x)\right ]\\ \text {Solve}\left [\frac {-b \log \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}-a-2 \sqrt {b^2} x\right )+\sqrt {b^2} \log \left (b \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}-a-2 \sqrt {b^2} x\right )\right )-\left (\sqrt {b^2}+b\right ) \log \left (\sqrt {a^2-4 a b x+4 b \left (b x^2+y(x)^2\right )}+a-2 \sqrt {b^2} x\right )}{2 \sqrt {b^2}}+\frac {\left (\sqrt {b^2}+b\right ) \log (y(x))}{b}=c_1,y(x)\right ]\\ y(x)&\to -\frac {i (2 b x-a)}{2 \sqrt {b}}\\ y(x)&\to \frac {i (2 b x-a)}{2 \sqrt {b}} \end{align*}

✗ Sympy

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

Timed Out