71.4.12 problem 12

Internal problem ID [14305]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.2, page 53
Problem number : 12
Date solved : Wednesday, March 05, 2025 at 10:44:48 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y^{\prime }&=-\frac {y}{x}+y^{{1}/{4}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

ode:=diff(y(x),x) = -y(x)/x+y(x)^(1/4); 
dsolve(ode,y(x), singsol=all);
 

\[ y^{{3}/{4}}-\frac {3 x}{7}-\frac {c_{1}}{x^{{3}/{4}}} = 0 \]

✓ Mathematica. Time used: 9.644 (sec). Leaf size: 31

ode=D[y[x],x]==-y[x]/x+y[x]^(1/4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {\left (3 x+\frac {7 c_1}{x^{3/4}}\right ){}^{4/3}}{7 \sqrt [3]{7}} \]

✓ Sympy. Time used: 102.810 (sec). Leaf size: 146

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x)**(1/4) + Derivative(y(x), x) + y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \frac {7^{\frac {2}{3}} \left (\frac {C_{1}}{x^{\frac {3}{4}}} + 3 x\right )^{\frac {4}{3}}}{49}, \ y{\left (x \right )} = \frac {7^{\frac {2}{3}} \sqrt [3]{\frac {7 C_{1}}{x^{\frac {3}{4}}} + 3 x} \left (- \frac {7 C_{1}}{x^{\frac {3}{4}}} - \frac {7 \sqrt {3} i C_{1}}{x^{\frac {3}{4}}} - 3 x - 3 \sqrt {3} i x\right )}{98}, \ y{\left (x \right )} = \frac {7^{\frac {2}{3}} \sqrt [3]{\frac {7 C_{1}}{x^{\frac {3}{4}}} + 3 x} \left (- \frac {7 C_{1}}{x^{\frac {3}{4}}} + \frac {7 \sqrt {3} i C_{1}}{x^{\frac {3}{4}}} - 3 x + 3 \sqrt {3} i x\right )}{98}\right ] \]