23.2.29 problem 30

Internal problem ID [5384]
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 : 30
Date solved : Tuesday, September 30, 2025 at 12:39:41 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}+a y^{\prime }+b&=0 \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 43

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

\begin{align*} y &= -\frac {x a}{2}-\frac {x \sqrt {a^{2}-4 b}}{2}+c_1 \\ y &= -\frac {x a}{2}+\frac {x \sqrt {a^{2}-4 b}}{2}+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 59

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

\begin{align*} y(x)&\to -\frac {1}{2} x \sqrt {a^2-4 b}-\frac {a x}{2}+c_1\\ y(x)&\to \frac {1}{2} x \sqrt {a^2-4 b}-\frac {a x}{2}+c_1 \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 44

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

\[ \left [ y{\left (x \right )} = C_{1} - \frac {a x}{2} - \frac {x \sqrt {a^{2} - 4 b}}{2}, \ y{\left (x \right )} = C_{1} - \frac {a x}{2} + \frac {x \sqrt {a^{2} - 4 b}}{2}\right ] \]