77.1.16 problem 30 (page 38)

Internal problem ID [17835]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 30 (page 38)
Date solved : Monday, March 31, 2025 at 04:35:27 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} x y^{\prime }-4 y&=x^{2} \sqrt {y} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=x*diff(y(x),x)-4*y(x) = x^2*y(x)^(1/2); 
dsolve(ode,y(x), singsol=all);
 

\[ \sqrt {y}-\frac {x^{2} \ln \left (x \right )}{2}-c_1 \,x^{2} = 0 \]

✓ Mathematica. Time used: 0.16 (sec). Leaf size: 21

ode=x*D[y[x],x]-4*y[x]==x^2*Sqrt[ y[x] ]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{4} x^4 (\log (x)+2 c_1){}^2 \]

✓ Sympy. Time used: 0.277 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*sqrt(y(x)) + x*Derivative(y(x), x) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{4} \left (C_{1}^{2} + C_{1} \log {\left (x \right )} + \frac {\log {\left (x \right )}^{2}}{4}\right ) \]