29.34.13 problem 1015

Internal problem ID [5584]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 34
Problem number : 1015
Date solved : Tuesday, March 04, 2025 at 10:31:33 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.056 (sec). Leaf size: 88

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

\begin{align*} y \left (x \right ) &= \frac {\left (3 b x +3 a \right ) \left (b x +a \right )^{{1}/{3}}+4 c_{1} b}{4 b} \\ y \left (x \right ) &= \frac {-3 \left (1+i \sqrt {3}\right ) \left (b x +a \right )^{{4}/{3}}+8 c_{1} b}{8 b} \\ y \left (x \right ) &= \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: 0.008 (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: 0.587 (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)
 

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