75.4.16 problem 61

Internal problem ID [16647]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 4. Equations with variables separable and equations reducible to them. Exercises page 38
Problem number : 61
Date solved : Monday, March 31, 2025 at 03:03:17 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.014 (sec). Leaf size: 24

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

\[ y = a \operatorname {RootOf}\left (\tan \left (\textit {\_Z} \right ) a -\textit {\_Z} a +c_1 -x \right )-c_1 \]

✓ Mathematica. Time used: 0.172 (sec). Leaf size: 114

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (-\frac {a^2}{a^2+x^2+K[2]^2+2 x K[2]}-\int _1^x\frac {a^2 (2 K[1]+2 K[2])}{\left (a^2+K[1]^2+K[2]^2+2 K[1] K[2]\right )^2}dK[1]+1\right )dK[2]+\int _1^x-\frac {a^2}{a^2+K[1]^2+y(x)^2+2 K[1] y(x)}dK[1]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 8.905 (sec). Leaf size: 34

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

\[ C_{1} + \frac {a \left (i \log {\left (- i a - x - y{\left (x \right )} \right )} - i \log {\left (i a - x - y{\left (x \right )} \right )}\right )}{2} - y{\left (x \right )} = 0 \]