23.1.238 problem 234

Internal problem ID [4845]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 234
Date solved : Tuesday, September 30, 2025 at 08:44:06 AM
CAS classification : [_linear]

\begin{align*} \left (a +x \right ) y^{\prime }&=2 \left (a +x \right )^{5}+3 y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=(x+a)*diff(y(x),x) = 2*(x+a)^5+3*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (2 a x +x^{2}+c_1 \right ) \left (a +x \right )^{3} \]

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 21

ode=(a+x)*D[y[x],x]==2*(a+x)^5+3*y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (a+x)^3 \left (2 a x+x^2+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.345 (sec). Leaf size: 63

from sympy import * 
x = symbols("x") 
a = symbols("a") 
y = Function("y") 
ode = Eq(-2*(a + x)**5 + (a + x)*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} a^{3} + 3 C_{1} a^{2} x + 3 C_{1} a x^{2} + C_{1} x^{3} + 2 a^{4} x + 7 a^{3} x^{2} + 9 a^{2} x^{3} + 5 a x^{4} + x^{5} \]