23.2.255 problem 270

Internal problem ID [5610]
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 : 270
Date solved : Tuesday, September 30, 2025 at 01:12:01 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{3}&=b x +a \end{align*}

✓ Maple. Time used: 0.031 (sec). Leaf size: 88

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

\begin{align*} y &= \frac {\left (3 b x +3 a \right ) \left (b x +a \right )^{{1}/{3}}+4 c_1 b}{4 b} \\ y &= \frac {-3 \left (1+i \sqrt {3}\right ) \left (b x +a \right )^{{4}/{3}}+8 c_1 b}{8 b} \\ y &= \frac {3 \left (i \sqrt {3}-1\right ) \left (b x +a \right )^{{4}/{3}}+8 c_1 b}{8 b} \\ \end{align*}

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 80

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

\begin{align*} y(x)&\to \frac {3 (a+b x)^{4/3}}{4 b}+c_1\\ y(x)&\to -\frac {3 \sqrt [3]{-1} (a+b x)^{4/3}}{4 b}+c_1\\ y(x)&\to \frac {3 (-1)^{2/3} (a+b x)^{4/3}}{4 b}+c_1 \end{align*}

✓ Sympy. Time used: 0.391 (sec). Leaf size: 68

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

\[ \left [ y{\left (x \right )} = C_{1} + \frac {3 \left (a + b x\right )^{\frac {4}{3}}}{4 b}, \ y{\left (x \right )} = C_{1} - \frac {3 i \left (\sqrt {3} - i\right ) \left (a + b x\right )^{\frac {4}{3}}}{8 b}, \ y{\left (x \right )} = C_{1} + \frac {3 i \left (\sqrt {3} + i\right ) \left (a + b x\right )^{\frac {4}{3}}}{8 b}\right ] \]