60.1.228 problem 233

Internal problem ID [10242]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 233
Date solved : Sunday, March 30, 2025 at 03:33:54 PM
CAS classification : [[_homogeneous, `class D`], _Bernoulli]

\begin{align*} x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right )&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 30

ode:=x*y(x)*diff(y(x),x)-y(x)^2+a*x^3*cos(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {-2 a \sin \left (x \right )+c_1}\, x \\ y &= -\sqrt {-2 a \sin \left (x \right )+c_1}\, x \\ \end{align*}

✓ Mathematica. Time used: 0.324 (sec). Leaf size: 58

ode=x*y[x]*D[y[x],x]-y[x]^2+a*x^3*Cos[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to -x \sqrt {2 \int _1^x-a \cos (K[1])dK[1]+c_1} \\ y(x)\to x \sqrt {2 \int _1^x-a \cos (K[1])dK[1]+c_1} \\ \end{align*}

✓ Sympy. Time used: 0.671 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(a*x**3*cos(x) + x*y(x)*Derivative(y(x), x) - y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = - x \sqrt {C_{1} - 2 a \sin {\left (x \right )}}, \ y{\left (x \right )} = x \sqrt {C_{1} - 2 a \sin {\left (x \right )}}\right ] \]