23.1.228 problem 224

Internal problem ID [4835]
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 : 224
Date solved : Tuesday, September 30, 2025 at 08:43:43 AM
CAS classification : [_linear]

\begin{align*} \left (1+x \right ) y^{\prime }&=x^{3} \left (4+3 x \right )+y \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=(1+x)*diff(y(x),x) = x^3*(3*x+4)+y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{4}+c_1 x +c_1 +x +1 \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 36

ode=(1+x)*D[y[x],x]==x^3*(4+3*x)+y[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (x+1) \left (\int _1^x\frac {K[1]^3 (3 K[1]+4)}{(K[1]+1)^2}dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.159 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3*(3*x + 4) + (x + 1)*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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